Modern Analysis

This book addresses real and abstract analysis, offering a sensible introduction to functional analysis as well as a thorough discussion of measure theory, Lebesgue integration, and related topics. Its topics include basic measure theory in an abstract and concrete form, material on classic linear functional analysis, probability, and basic results used in the theory of partial differential equations. Two different proofs of the central limit theorem are examined as well as a straightforward approach to conditional probability and expectation.