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 of this title include the core subjects of real analysis and 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.
Euclidean spaces and the Riemann integral Lebesgue measure on Euclidean spaces The Lebesgue integral on Euclidean spaces Differentiation Measures in abstract spaces Lebesgue spaces and continuous functions Schwartz space and distributions Fourier analysis Wavelet analysis Appendix A Appendix B Solutions to problems Bibliography Index.