Real analysis with an introduction to wavelets and applications 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 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