Volumes I through V of Theorems and Problems in Functional Analysis: The Answer Book present different techniques for solving the 828 Exercises found in the A.A. Kirillov and Gvichiani book, entitled Theorems and Problems in Functional Analysis. The original book by Kirillov and Gvichiani was in the Problem Book in Mathematics Series, published by Springer.

This volume mainly focuses on integral theory and measure theory.  It covers problems with set algebras, the measure of Lebesgue, the caratheodory measurability, the extension of measure, construction of measures such as the Wiener measure, measurable functions, Lusine's theorem, and the Dirichlet function.  The last part of the volume deals with the Lebesgue-Stieljes integral.

Supplementing the book, Theorems and Problems in Functional Analysis, these volumes may be used by graduate students taking a course in functional analysis.  In order to understand this text, the reader must be familiar with mathematical analysis and real analysis.