Diccionario politécnico Beigbeder
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This textbook begins with the fundamentals of classical real variables and leads to Lebesgue's definition of the integral, the theory of integration and the structure of measures in a measure theoretical format. The core chapters are followed by chapters of a topical nature, which illuminate the authors' intellectual vision of modern real analysis. These topics include weak convergence, the Riesz representation theorem, the Lebesgue differential theorem, and self-similar sets and fractals. Historical remarks, illuminating problems and examples, and appendices on functional analysis and Fourier analysis provide insight into the theory and its applications. The self-contained and fundamental coverage of the theories of integration, differentiation, and modern analysis make this text ideal for graduate students in the classroom setting.
INDICE: Preface.- Classical real variables.- Lebesgue measure and general measure theory.- The Lebesgue integral.- The relationship between differentiation and integration on R.- Spaces of measures and the Radon–Nikodym theorem.- Weak convergence of measures.- Riesz representation theorem.- Lebesgue differentiation theorem on R.- Self-similar sets and fractals.- Appendix I: Functional analysis.- Appendix II: Fourier Analysis.- References.- Index.
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