Exercises in Analysis

Leszek Gasińksi is the Chair of Optimization and Control Theory in the Institute of Computer Science at Jagiellonian University in Krakow, Poland. He is the co-author, along with Nikolaos S. Papageorgiou, of "Nonlinear Analysis" (CRC 2005) and "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems" (CRC 2006). Nikolaos S. Papageorgiou is a Professor of Mathematics in the School of Applied Mathematical and Physical Sciences at National Technical University in Athens, Greece. He is the co-author, along with Leszek Gasińksi, of "Nonlinear Analysis" (CRC 2005) and "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems" (CRC 2006).

• 1. Metric Spaces.- 2. Topological Spaces.- 3. Measure, Integral, and Martingales.- 4. Measures and Topology.- 5. Functional Analysis.- Other Problem Books.- List of Symbols.- Index.

"The book presents most standard theorems in real analysis, topology and functional analysis as well as a variety of problems with their solutions. ... The presentation is lucid and elegant. The notations are standard throughout the text. ... useful to graduate students and faculty whose interests are in probability, finance, measure theory, topology, partial differential equations and operator theory ... . Such a book certainly must live in every library where other mathematics books in the similar topics reside." (Dhruba Adhikari, MAA Reviews, maa.org, December, 2015) "The topics covered will carry almost any serious student from advanced undergraduate mathematics all the way through graduate qualifying examinations ... . Summing Up: Recommended. Upper-division undergraduates and graduate students." (D. V. Feldman, Choice, Vol. 52 (9), May, 2015) "This volume is a collection of interesting problems in real analysis and functional analysis. It is addressed to advanced undergraduate and graduate students as well as to researchers in pure and applied analysis. ... The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic. The reviewer highly recommends this book to all mathematical libraries." (Vicentiu D. Radulescu, zbMATH, Vol. 1298, 2014)