Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum's approach is designed to appeal to intuition whenever possible. Modern Real and Complex Analysis provides up-to-date treatment of such subjects as the Daniell integration, differentiation, functional analysis and Banach algebras, conformal mapping and Bergman's kernels, defective functions, Riemann surfaces and uniformization, and the role of convexity in analysis. The text supplies an abundance of exercises and illustrative examples to reinforce learning, and extensive notes and remarks to help clarify important points.
**
From the Publisher
Using a contemporary approach and a lively style, Gelbaum combines real and complex analysis, covering all major topics. He discusses topology in three ways: via open sets, nets and filters. Features a detailed exploration of the link between measure as derived from a Daniell functional and classical Lebesgue-Caratheodory measure. Includes complete definitions of all mathematical concepts as well as numerous exercises and illustrations.
From the Back Cover
Modern Real and Complex Analysis
Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum's approach is designed to appeal to intuition whenever possible. Modern Real and Complex Analysis provides up-to-date treatment of such subjects as the Daniell integration, differentiation, functional analysis and Banach algebras, conformal mapping and Bergman's kernels, defective functions, Riemann surfaces and uniformization, and the role of convexity in analysis. The text supplies an abundance of exercises and illustrative examples to reinforce learning, and extensive notes and remarks to help clarify important points.
Description:
Modern Real and Complex Analysis
Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum's approach is designed to appeal to intuition whenever possible. Modern Real and Complex Analysis provides up-to-date treatment of such subjects as the Daniell integration, differentiation, functional analysis and Banach algebras, conformal mapping and Bergman's kernels, defective functions, Riemann surfaces and uniformization, and the role of convexity in analysis. The text supplies an abundance of exercises and illustrative examples to reinforce learning, and extensive notes and remarks to help clarify important points.
**
From the Publisher
Using a contemporary approach and a lively style, Gelbaum combines real and complex analysis, covering all major topics. He discusses topology in three ways: via open sets, nets and filters. Features a detailed exploration of the link between measure as derived from a Daniell functional and classical Lebesgue-Caratheodory measure. Includes complete definitions of all mathematical concepts as well as numerous exercises and illustrations.
From the Back Cover
Modern Real and Complex Analysis
Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum's approach is designed to appeal to intuition whenever possible. Modern Real and Complex Analysis provides up-to-date treatment of such subjects as the Daniell integration, differentiation, functional analysis and Banach algebras, conformal mapping and Bergman's kernels, defective functions, Riemann surfaces and uniformization, and the role of convexity in analysis. The text supplies an abundance of exercises and illustrative examples to reinforce learning, and extensive notes and remarks to help clarify important points.