Edisi luring mata kuliah

Haar measure and quotient integration

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Pelajaran

  1. measure-and-hilbert-space-tools: Measure and Hilbert space tools for Haar integration
    Halaman PDF 4 · EPUB: EPUB/text/ch002.xhtml#measure-and-hilbert-space-tools
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    • Measure and Hilbert space tools for Haar integration
      measure-and-hilbert-space-tools-for-haar-integration
      Buka lokasi PDF yang tepat · Halaman PDF 4
      EPUB: EPUB/text/ch002.xhtml#measure-and-hilbert-space-tools
    • 1. From an outer measure to a measure
      1-from-an-outer-measure-to-a-measure
      Buka lokasi PDF yang tepat · Halaman PDF 5
      EPUB: EPUB/text/ch002.xhtml#measure-and-hilbert-space-tools--1-from-an-outer-measure-to-a-measure
    • 2. Integration and convergence without countability assumptions
      2-integration-and-convergence-without-countability-assumptions
      Buka lokasi PDF yang tepat · Halaman PDF 6
      EPUB: EPUB/text/ch002.xhtml#measure-and-hilbert-space-tools--2-integration-and-convergence-without-countability-assumptions
    • 3. The complete spaces of integrable functions
      3-the-complete-spaces-of-integrable-functions
      Buka lokasi PDF yang tepat · Halaman PDF 7
      EPUB: EPUB/text/ch002.xhtml#measure-and-hilbert-space-tools--3-the-complete-spaces-of-integrable-functions
    • 4. Densities and bounded functionals
      4-densities-and-bounded-functionals
      Buka lokasi PDF yang tepat · Halaman PDF 7
      EPUB: EPUB/text/ch002.xhtml#measure-and-hilbert-space-tools--4-densities-and-bounded-functionals
    • Why sigma-finiteness matters for a density
      radon-nikodym-countability
      Buka lokasi PDF yang tepat · Halaman PDF 8
      EPUB: EPUB/text/ch002.xhtml#measure-and-hilbert-space-tools--radon-nikodym-countability
    • 5. Tensor products as Hilbert–Schmidt operators
      5-tensor-products-as-hilbert-schmidt-operators
      Buka lokasi PDF yang tepat · Halaman PDF 9
      EPUB: EPUB/text/ch002.xhtml#measure-and-hilbert-space-tools--5-tensor-products-as-hilbert-schmidt-operators
    • 6. One-variable integral identities
      6-one-variable-integral-identities
      Buka lokasi PDF yang tepat · Halaman PDF 10
      EPUB: EPUB/text/ch002.xhtml#measure-and-hilbert-space-tools--6-one-variable-integral-identities
    • 7. Exercises with complete solutions
      7-exercises-with-complete-solutions
      Buka lokasi PDF yang tepat · Halaman PDF 10
      EPUB: EPUB/text/ch002.xhtml#measure-and-hilbert-space-tools--7-exercises-with-complete-solutions
    • What this enables
      what-this-enables
      Buka lokasi PDF yang tepat · Halaman PDF 11
      EPUB: EPUB/text/ch002.xhtml#measure-and-hilbert-space-tools--what-this-enables
    • References
      references
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      EPUB: EPUB/text/ch002.xhtml#measure-and-hilbert-space-tools--references
  2. haar-measure-on-locally-compact-groups: Haar measure on locally compact groups
    Halaman PDF 11 · EPUB: EPUB/text/ch003.xhtml#haar-measure-on-locally-compact-groups
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  3. quotient-measures-and-weils-integration-formula: Quotient measures and Weil's integration formula
    Halaman PDF 39 · EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula
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    • Quotient measures and Weil's integration formula
      quotient-measures-and-weil-s-integration-formula
      Buka lokasi PDF yang tepat · Halaman PDF 39
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula
    • What to know first
      what-to-know-first
      Buka lokasi PDF yang tepat · Halaman PDF 40
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--what-to-know-first
    • Local topology and compactly supported functions
      local-topology-and-compactly-supported-functions
      Buka lokasi PDF yang tepat · Halaman PDF 40
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--local-topology-and-compactly-supported-functions
    • Averaging along the subgroup
      averaging-along-the-subgroup
      Buka lokasi PDF yang tepat · Halaman PDF 41
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--averaging-along-the-subgroup
    • Exactly when the quotient measure is invariant
      exactly-when-the-quotient-measure-is-invariant
      Buka lokasi PDF yang tepat · Halaman PDF 42
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--exactly-when-the-quotient-measure-is-invariant
    • A cutoff over all cosets
      a-cutoff-over-all-cosets
      Buka lokasi PDF yang tepat · Halaman PDF 43
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--a-cutoff-over-all-cosets
    • The modular density and weighted integration
      the-modular-density-and-weighted-integration
      Buka lokasi PDF yang tepat · Halaman PDF 43
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--the-modular-density-and-weighted-integration
    • Quasi-invariance and the direction of translation
      quasi-invariance-and-the-direction-of-translation
      Buka lokasi PDF yang tepat · Halaman PDF 45
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--quasi-invariance-and-the-direction-of-translation
    • Relative invariance and a character
      relative-invariance-character
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      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--relative-invariance-character
    • The quasi-regular representation
      quasi-regular-representation
      Buka lokasi PDF yang tepat · Halaman PDF 46
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--quasi-regular-representation
    • Finite covolume forces unimodularity
      finite-covolume-unimodularity
      Buka lokasi PDF yang tepat · Halaman PDF 47
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--finite-covolume-unimodularity
    • Integration of quotient densities
      quotient-density-integral
      Buka lokasi PDF yang tepat · Halaman PDF 47
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--quotient-density-integral
    • Examples that test the formula
      examples-that-test-the-formula
      Buka lokasi PDF yang tepat · Halaman PDF 48
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--examples-that-test-the-formula
    • Exercises with solutions
      exercises-with-solutions
      Buka lokasi PDF yang tepat · Halaman PDF 49
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--exercises-with-solutions
    • What this enables
      what-this-enables
      Buka lokasi PDF yang tepat · Halaman PDF 50
      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--what-this-enables
    • Sources and credit
      sources-and-credit
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      EPUB: EPUB/text/ch004.xhtml#quotient-measures-and-weils-integration-formula--sources-and-credit
  4. finite-covolume-and-arithmetic-quotients: Finite covolume and arithmetic quotients
    Halaman PDF 51 · EPUB: EPUB/text/ch005.xhtml#finite-covolume-and-arithmetic-quotients
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    • Finite covolume and arithmetic quotients
      finite-covolume-and-arithmetic-quotients
      Buka lokasi PDF yang tepat · Halaman PDF 51
      EPUB: EPUB/text/ch005.xhtml#finite-covolume-and-arithmetic-quotients
    • What to know first
      what-to-know-first
      Buka lokasi PDF yang tepat · Halaman PDF 51
      EPUB: EPUB/text/ch005.xhtml#finite-covolume-and-arithmetic-quotients--what-to-know-first
    • 1. Two integer reductions
      1-two-integer-reductions
      Buka lokasi PDF yang tepat · Halaman PDF 51
      EPUB: EPUB/text/ch005.xhtml#finite-covolume-and-arithmetic-quotients--1-two-integer-reductions
    • Borel fundamental domains and covolume
      borel-fundamental-domain
      Buka lokasi PDF yang tepat · Halaman PDF 52
      EPUB: EPUB/text/ch005.xhtml#finite-covolume-and-arithmetic-quotients--borel-fundamental-domain
    • 2. A fundamental region in the upper half-plane
      2-a-fundamental-region-in-the-upper-half-plane
      Buka lokasi PDF yang tepat · Halaman PDF 53
      EPUB: EPUB/text/ch005.xhtml#finite-covolume-and-arithmetic-quotients--2-a-fundamental-region-in-the-upper-half-plane
    • 3. From area to group covolume
      3-from-area-to-group-covolume
      Buka lokasi PDF yang tepat · Halaman PDF 54
      EPUB: EPUB/text/ch005.xhtml#finite-covolume-and-arithmetic-quotients--3-from-area-to-group-covolume
    • 4. Additive rational adèles
      4-additive-rational-adèles
      Buka lokasi PDF yang tepat · Halaman PDF 55
      EPUB: EPUB/text/ch005.xhtml#finite-covolume-and-arithmetic-quotients--4-additive-rational-adèles
    • 5. Norm-one rational idèles
      5-norm-one-rational-idèles
      Buka lokasi PDF yang tepat · Halaman PDF 55
      EPUB: EPUB/text/ch005.xhtml#finite-covolume-and-arithmetic-quotients--5-norm-one-rational-idèles
    • Heisenberg lattice volume
      heisenberg-lattice-volume
      Buka lokasi PDF yang tepat · Halaman PDF 56
      EPUB: EPUB/text/ch005.xhtml#finite-covolume-and-arithmetic-quotients--heisenberg-lattice-volume
    • 6. Exercises with complete solutions
      6-exercises-with-complete-solutions
      Buka lokasi PDF yang tepat · Halaman PDF 57
      EPUB: EPUB/text/ch005.xhtml#finite-covolume-and-arithmetic-quotients--6-exercises-with-complete-solutions
    • References and relation to the programme
      references-and-relation-to-the-programme
      Buka lokasi PDF yang tepat · Halaman PDF 57
      EPUB: EPUB/text/ch005.xhtml#finite-covolume-and-arithmetic-quotients--references-and-relation-to-the-programme
  5. weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian: Weak topologies: Tychonoff, Banach–Alaoglu, Mazur, bipolars, Krein–Milman and Eberlein–Šmulian
    Bab prasyarat
    Halaman PDF 57 · EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian
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    • Weak topologies: Tychonoff, Banach–Alaoglu, Mazur, bipolars, Krein–Milman and Eberlein–Šmulian
      weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-šmulian
      Buka lokasi PDF yang tepat · Halaman PDF 57
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian
    • Conventions
      conventions
      Buka lokasi PDF yang tepat · Halaman PDF 58
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--conventions
    • 1. Weak topologies
      OA-FND-WT-01
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      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--OA-FND-WT-01
    • oa-fnd-wt-01
      oa-fnd-wt-01
      Buka lokasi PDF yang tepat · Halaman PDF 58
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--oa-fnd-wt-01
    • 2. Tychonoff's theorem
      OA-FND-WT-02
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      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--OA-FND-WT-02
    • oa-fnd-wt-02
      oa-fnd-wt-02
      Buka lokasi PDF yang tepat · Halaman PDF 58
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--oa-fnd-wt-02
    • 3. The Banach–Alaoglu theorem
      OA-FND-WT-03
      Buka lokasi PDF yang tepat · Halaman PDF 59
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--OA-FND-WT-03
    • oa-fnd-wt-03
      oa-fnd-wt-03
      Buka lokasi PDF yang tepat · Halaman PDF 59
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--oa-fnd-wt-03
    • 4. Mazur's theorem
      OA-FND-WT-04
      Buka lokasi PDF yang tepat · Halaman PDF 60
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--OA-FND-WT-04
    • oa-fnd-wt-04
      oa-fnd-wt-04
      Buka lokasi PDF yang tepat · Halaman PDF 60
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--oa-fnd-wt-04
    • 5. Annihilators, bipolars and Goldstine's theorem
      OA-FND-WT-05
      Buka lokasi PDF yang tepat · Halaman PDF 60
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--OA-FND-WT-05
    • oa-fnd-wt-05
      oa-fnd-wt-05
      Buka lokasi PDF yang tepat · Halaman PDF 60
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--oa-fnd-wt-05
    • 6. The Krein–Milman theorem
      OA-FND-WT-06
      Buka lokasi PDF yang tepat · Halaman PDF 61
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--OA-FND-WT-06
    • oa-fnd-wt-06
      oa-fnd-wt-06
      Buka lokasi PDF yang tepat · Halaman PDF 61
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--oa-fnd-wt-06
    • 7. The Eberlein–Šmulian theorem
      OA-FND-WT-07
      Buka lokasi PDF yang tepat · Halaman PDF 62
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--OA-FND-WT-07
    • oa-fnd-wt-07
      oa-fnd-wt-07
      Buka lokasi PDF yang tepat · Halaman PDF 62
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--oa-fnd-wt-07
    • Exercises
      exercises
      Buka lokasi PDF yang tepat · Halaman PDF 63
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--exercises
    • Where this leads
      where-this-leads
      Buka lokasi PDF yang tepat · Halaman PDF 64
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--where-this-leads
    • References
      references
      Buka lokasi PDF yang tepat · Halaman PDF 64
      EPUB: EPUB/text/ch006.xhtml#weak-topologies-tychonoff-banach-alaoglu-mazur-bipolars-krein-milman-and-eberlein-smulian--references
  6. hilbert-spaces-and-compact-operators: Hilbert spaces and compact operators
    Bab prasyarat
    Halaman PDF 65 · EPUB: EPUB/text/ch007.xhtml#hilbert-spaces-and-compact-operators
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  7. the-stone-weierstrass-theorem-for-functions-vanishing-at-infinity: The Stone–Weierstrass theorem for functions vanishing at infinity
    Bab prasyarat
    Halaman PDF 74 · EPUB: EPUB/text/ch008.xhtml#the-stone-weierstrass-theorem-for-functions-vanishing-at-infinity
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  8. NT-ADL-01: Restricted products and profinite completions
    Bab prasyarat
    Halaman PDF 99 · EPUB: EPUB/text/ch009.xhtml#NT-ADL-01
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  9. NT-ADL-02: The adèle ring of a number field
    Bab prasyarat
    Halaman PDF 108 · EPUB: EPUB/text/ch010.xhtml#NT-ADL-02
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  10. NT-ADL-03: Idèles and the idèle class group
    Bab prasyarat
    Halaman PDF 118 · EPUB: EPUB/text/ch011.xhtml#NT-ADL-03
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  11. NT-LOC-02: Completions, the p-adic numbers and complete discretely valued fields
    Bab prasyarat
    Halaman PDF 127 · EPUB: EPUB/text/ch012.xhtml#NT-LOC-02
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  12. fremlin-neighbourhood-uniqueness: Haar uniqueness through shrinking neighborhoods
    Suplemen editorial
    Halaman PDF 137 · EPUB: EPUB/text/ch013.xhtml#fremlin-neighbourhood-uniqueness
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Edisi dan sumber

Kutipan keterangan sumber asli

Includes all four lessons, all seven bundled prerequisite chapters and the Fremlin-derived supplementary proof. It is not the complete harmonic-analysis course, and further reading listed by the source remains outside this companion. The four course lessons and seven bundled programme chapters are CC0 1.0, with all original human source credits and AI author statements retained. The supplementary proof Haar uniqueness through shrinking neighborhoods adapts D. H. Fremlin and remains under the Design Science License. Its source and change notices accompany the proof, and the complete licence is included. This mixed collection does not relicense Fremlin’s work as CC0.

Atribusi asli dan atribusi konversi format

Claude Opus 5.5 (Anthropic; original Haar lesson, effort not recorded); OpenAI Codex — GPT-6 Astra, Ultra (quotient lesson); GPT-6.1 Sol, Ultra (measure tools, arithmetic integration, corrections and self-check). Each bundled chapter retains its own author statement. OpenAI Codex — GPT-6 Astra, Ultra effort (source-preserving format conversion)

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