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

Academic Press – 2004, 392 pages
ISBN: 0123548616, 9780123548610An 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. (Amazon).
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 analysisPraface
Fundamentals
Measure Theory
The Lebesgue Integral
Special Topics of Lebesgue Integral and Applications
Vector Spaces, Hilbert Spaces, and the L2 Space
Fourier Analysis
Orthonormal Wavelet Bases
Compactly Supported Wavelets
Wavelets in Signal Processing
Appendix