Introduction to Measure Theory and Functional Analysis

✍ Scribed by Piermarco Cannarsa, Teresa D'Aprile (auth.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 314
• Series: UNITEXT 89
• Edition: 1
• Category: Library

✦ Synopsis

This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two courses, it can be supplemented by additional topics from the third part of the book, such as functions of bounded variation, absolutely continuous functions, and signed measures.

This textbook addresses the needs of graduate students in mathematics, who will find the basic material they will need in their future careers, as well as those of researchers, who will appreciate the self-contained exposition which requires no other preliminaries than basic calculus and linear algebra.

✦ Table of Contents

Front Matter....Pages i-xiv
Front Matter....Pages 1-1
Measure Spaces....Pages 3-35
Integration....Pages 37-80
(L^p) Spaces....Pages 81-106
Product Measures....Pages 107-130
Front Matter....Pages 131-131
Hilbert Spaces....Pages 133-166
Banach Spaces....Pages 167-225
Front Matter....Pages 227-227
Absolutely Continuous Functions....Pages 229-252
Signed Measures....Pages 253-270
Set-Valued Functions....Pages 271-277
Back Matter....Pages 279-314

✦ Subjects

Measure and Integration; Functional Analysis; Probability Theory and Stochastic Processes; Quantitative Finance; Mathematical Applications in the Physical Sciences; Mathematical Methods in Physics