Robert Gardner & Don Hong 
Real Analysis with an Introduction to Wavelets and Applications [PDF ebook] 

Real Analysis with an Introduction to Wavelets and Applications is 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