Harmonic analysis on locally compact groups

Haar integration on arbitrary locally compact groups, closed-subgroup quotient measures, and arithmetic covolumes. Human sources and AI authorship are credited in each lesson.

1. Measure and Hilbert space tools for Haar integration
2. Haar measure on locally compact groups
3. Quotient measures and Weil's integration formula
4. Finite covolume and arithmetic quotients

Source companion: Haar uniqueness through shrinking neighborhoods. The complete proof is in Haar Theorem9.2; the companion records its source, conventions and Design Science License.

Prerequisite chapters: Weak topologies: Tychonoff, Banach–Alaoglu, Mazur, bipolars, Krein–Milman and Eberlein–Šmulian, Hilbert spaces and compact operators, The Stone–Weierstrass theorem for functions vanishing at infinity, Restricted products and profinite completions, The rational adèle ring and its compact quotient, Rational idèles and their compact norm-one quotient, Completions, the p-adic numbers and complete discretely valued fields

Free-source and internal-proof policy · Internal proof map · Sources and authorship