Hong D., Wang J., Gardner R. Real Analysis with an Introduction to Wavelets

Academic Press, 2004. - 392 pages.
An in-depth look at real analysis and its applications, including an introduction to wavelet analysis, a popular topic in "applied real analysis". This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral, harmonic analysis and wavelet theory with many associated applications..
*The text is relatively elementary at the start, but the level of difficulty steadily increases.
*The book contains many clear, detailed examples, case studies and exercises.
*Many real world applications relating to measure theory and pure analysis.
*Introduction to wavelet analysis.