Mathematical Analysis II

This final text in the Zakon Series on Mathematics Analysis completes the material on Real Analysis that is the foundation for later courses in functional analysis, harmonic analysis, probability theory, etc.

**Tag(s):**
Mathematics

**Publication date**: 31 Dec 2009

**ISBN-10**:
1931705038

**ISBN-13**:
n/a

**Paperback**:
424 pages

**Views**: 17,278

Mathematical Analysis II

This final text in the Zakon Series on Mathematics Analysis completes the material on Real Analysis that is the foundation for later courses in functional analysis, harmonic analysis, probability theory, etc.

Terms and Conditions:

Excerpts from the Description:

The Trillia Group wrote:Terms and Conditions: All uses of this text are subject to the Terms and Conditions contained in this text. As part of these terms, we offer this text free of charge to students using it for self-study, and to lecturers evaluating it as a required or recommended text for a course. All other uses of this text are subject to a charge of $10US for individual use and $300US for use by all individuals at a single site of a college or university.

Excerpts from the Description:

The Trillia Group wrote:This final text in the Zakon Series on Mathematics Analysis follows the release of the author's Basic Concepts of Mathematics and Mathematical Analysis I and completes the material on Real Analysis that is the foundation for later courses in functional analysis, harmonic analysis, probability theory, etc. The first chapter extends calculus to n-dimensional Euclidean space and, more generally, Banach spaces, covering the inverse function theorem, the implicit function theorem, Taylor expansions, etc. Some basic theorems in functional analysis, including the open mapping theorem and the Banach-Steinhaus uniform boundedness principle, are also proved. The text then moves to measure theory, with a complete discussion of outer measures, Lebesgue measure, Lebesgue-Stieltjes measures, and differentiation of set functions. The discussion of measurable functions and integration in the following chapter follows an innovative approach, carefully choosing one of the equivalent definitions of measurable functions that allows the most intuitive development of the material. Fubini's theorem, the Radon-Nikodym theorem, and the basic convergence theorems (Fatou's lemma, the monotone convergence theorem, dominated convergence theorem) are covered. Finally, a chapter relates antidifferentiation to Lebesgue theory, Cauchy integrals, and convergence of parametrized integrals. Nearly 500 exercises allow students to develop their skills in the area.

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