Description
Book SynopsisOffers a treatment of measure and integration that begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. This text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales.
Table of ContentsThe Riemann integral Lebesgue measure on the line Integration on measure spaces $L^p$ spaces The Caratheodory construction of measures Product measures Lebesgue measure on $\mathbb{R}^n$ and on manifolds Signed measures and complex measures $L^p$ spaces, II Sobolev spaces Maximal functions and a.e. phenomena Hausdorff's $r$-dimensional measures Radon measures Ergodic theory Probability spaces and random variables Wiener measure and Brownian motion Conditional expectation and martingales Metric spaces, topological spaces, and compactness Derivatives, diffeomorphisms, and manifolds The Whitney Extension Theorem The Marcinkiewicz Interpolation Theorem Sard's Theorem A change of variable theorem for many-to-one maps Integration of differential forms Change of variables revisited The Gauss-Green formula on Lipschitz domains Bibliography Symbol index Subject index.
