Prerequisites and supporting reading

The Hermite lesson uses the following already-public programme proofs. Its broad Measure and Integration curriculum link is orientation; the first three entries give the actual integration providers.

• Section 1: Lebesgue outer measure and completed measure
• Section 2, Theorems 2.1–2.2: monotone and dominated convergence
• Theorem 5.1(4), (5), (7): Tonelli, Fubini and agreement with ordinary products in the sigma-compact second-countable setting
• Parseval and Hilbert orthonormal bases
• Baire category theorem
• Fourier uniqueness

Section 6 also uses the exterior-algebra definitions, Lemma 3.1 and the full algebraic Lemma 4.1 from the Bott-operator lesson, included here as exact excerpts. No result from the rest of that lesson is used for this algebraic step.

The full Bott/index and totally characteristic operator lessons are onward applications, not included course editions. The Bott links open the limited supporting excerpt; the unavailable totally characteristic title is displayed as text.