Measure, Integration & Real Analysis — Axler

Sheldon Axler (Springer GTM 282, open access)

Measure theory and Lebesgue integration built toward Hilbert spaces and Fourier analysis: outer and Lebesgue measure, measurable functions and their convergence, integration and the limit theorems, product measures and iterated integrals, the \(\mathcal{L}^p\)/\(L^p\) spaces, inner product spaces and orthonormal bases, and Fourier series and the Fourier transform on \(L^1\) and \(L^2\). Core text for Course 1 Section 5 — the measure-theoretic footing under probability, distributions, and functional analysis, where \(L^2\) is the signal space of DSP.

Chapters

Exercises added as I work through each chapter.