Front Cover -- Real Analysis with an Introduction to Wavelets and Applications -- Copyright Page -- Contents -- Preface -- Chapter I. Fundamentals -- 1 Elementary Set Theory -- 2 Relations and Orderings -- 3 Cardinality and Countability -- 4 The Topology of Rn -- Chapter 2. Measure Theory -- 1 Classes of Sets -- 2 Measures on a Ring -- 3 Outer Measures and Lebesgue Measure -- 4 Measurable Functions -- 5 Convergence of Measurable Functions -- Chapter 3. The Lebesgue integral -- 1 Riemann Integral and Lebesgue Integral -- 2 The General Lebesgue Integral -- 3 Convergence and Approximation of Lebesgue Integrals -- 4 Lebesgue Integrals in the Plane -- Chapter 4. Special Topics of Lebesgue Integral and Applications -- 1 Differentiation and Integration -- 2 Mathematical Models for Probability -- 3 Convergence and Limit Theorems -- Chapter 5. Vector Spaces, Hilbert Spaces, and the L2 Space -- 1 Groups, Fields, and Vector Spaces -- 2 Inner Product Spaces -- 3 The Space L2 -- 4 Projections and Hilbert Space Isomorphisms -- 5 Banach Spaces -- Chapter 6. Fourier Analysis -- 1 Fourier Series -- 2 Parseval's Formula -- 3 The Fourier Transform of Integrable Functions -- 4 Fourier Transforms of Square Integrable Functions -- 5 The Poisson Summation Formula -- Chapter 7. Orthonormal Wavelet Bases -- 1 Haar Wavelet Basis -- 2 Multiresolution Analysis -- 3 Orthonormal Wavelets from MRA -- 4 Orthonormal Spline Wavelets -- 5 Fast Wavelet Transforms -- 6 Biorthogonal Wavelet Bases -- Chapter 8. Compactly Supported Wavelets -- 1 Symbols of Orthonormal Scaling Functions -- 2 The Daubechies Scaling Functions -- 3 Computation of Daubechies Scaling Fimctions -- 4 Wavelet Packets -- 5 Compactly Supported Biorthogonal Wavelet Bases -- Chapter 9. Wavelets In Signal Processing -- 1 Signals -- 2 Filters -- 3 Coding Signals by Wavelet Transform -- 4 Filter Banks -- Appendix.

Biliography -- Index.