An introduction to analysis with the right mix of abstract theories
and concrete problems. Starting with general measure theory, the
book goes on to treat Borel and Radon measures and introduces the
reader to Fourier analysis in Euclidean spaces with a treatment of
Sobolev spaces, distributions, and the corresponding Fourier
analysis. It continues with a Hilbertian treatment of the basic
laws of probability including Doob's martingale convergence theorem
and finishes with Malliavin's "stochastic calculus of variations"
developed in the context of Gaussian measure spaces. This
invaluable contribution gives a taste of the fact that analysis is
not a collection of independent theories, but can be treated as a
whole.
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