Real Analysis--With an Introduction to Wavelet Theory (Translations of Mathematical Monographs)

This introduction to real analysis is based on a series of lectures by the author at Tohoku University. The text covers real numbers, the notion of general topology, and a brief treatment of the Riemann integral, followed by chapters on the classical theory of the Lebesgue integral on Euclidean spaces; the differentiation theorem and functions of bounded variation; Lebesgue spaces; distribution theory; the classical theory of the Fourier transform and Fourier series; and wavelet theory. Features: The core subjects of real analysis. The fundamentals for students who are interested in harmonic analysis, probability or partial differential equations. This volume would be a suitable textbook for an advanced undergraduate or first year graduate course in analysis.

The presentation is clear and rigorous.
SIAM Revie