Clear, accessible text for a 1st course in abstract analysis, suitable for undergraduates with a good background in the calculus of functions of 1 and several variables. Sets and relations, real number system and linear spaces, normed spaces, normed linear spaces, Lebesque integral, approximation theory, Banach fixed-point theorem, Stieltjes integrals, more. Includes problems.
Here's a sample of other books in this Dover category
Introductory Real Analysis by A. N. Kolmogorov, S. V. Fomin Comprehensive, elementary introduction to real and functional analysis. Covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. Features 350 problems.
Counterexamples in Analysis by Bernard R. Gelbaum, John M. H. Olmsted These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
Real-Variable Methods in Harmonic Analysis by Alberto Torchinsky This text starts with Fourier series, summability, norm convergence, and conjugate function. Additional topics include Hilbert transform, Paley theory, Cauchy integrals on Lipschitz curves, and boundary value problems. 1986 edition.
Real Variables with Basic Metric Space Topology by Robert B. Ash Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition.
