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Lebesgue Integration
This concise introduction to Lebesgue integration is geared toward advanced undergraduate math majors and may be read by any student possessing some familiarity with real variable theory and elementary calculus. The self-contained treatment features exercises at the end of each chapter that range from simple to difficult.
The approach begins with sets and functions and advances to Lebesgue measure, including considerations of measurable sets, sets of measure zero, and Borel sets and nonmeasurable sets. A two-part exploration of the integral covers measurable functions, convergence theorems, convergence in mean, Fourier theory, and other topics. A chapter on calculus examines change of variables, differentiation of integrals, and integration of derivatives and by parts. The text concludes with a consideration of more general measures, including absolute continuity and convolution products.
The approach begins with sets and functions and advances to Lebesgue measure, including considerations of measurable sets, sets of measure zero, and Borel sets and nonmeasurable sets. A two-part exploration of the integral covers measurable functions, convergence theorems, convergence in mean, Fourier theory, and other topics. A chapter on calculus examines change of variables, differentiation of integrals, and integration of derivatives and by parts. The text concludes with a consideration of more general measures, including absolute continuity and convolution products.
Reprint of the Holt, Rinehart & Winston, New York, 1962 edition.
mathematics, calculus, math majors, advanced math, undergraduate students, real variable theory, helpful exercises, sets and functions, measurable sets, sets of measure zero, borel sets, nonmeasurable sets, integrals, convergence theorems, convergence in mean, fourier theory, change of variables, differentiation, derivatives, general measures, continuity, convolution, young frechet approach, fubinis theorems, complex and vector functions, approximations to integrable functions, integration;Lebesgue Integration; Lebesgue Measure; Fourier Theory; Borel Measures; Fourier Transforms$4.53
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Description
This concise introduction to Lebesgue integration is geared toward advanced undergraduate math majors and may be read by any student possessing some familiarity with real variable theory and elementary calculus. The self-contained treatment features exercises at the end of each chapter that range from simple to difficult.
The approach begins with sets and functions and advances to Lebesgue measure, including considerations of measurable sets, sets of measure zero, and Borel sets and nonmeasurable sets. A two-part exploration of the integral covers measurable functions, convergence theorems, convergence in mean, Fourier theory, and other topics. A chapter on calculus examines change of variables, differentiation of integrals, and integration of derivatives and by parts. The text concludes with a consideration of more general measures, including absolute continuity and convolution products.
The approach begins with sets and functions and advances to Lebesgue measure, including considerations of measurable sets, sets of measure zero, and Borel sets and nonmeasurable sets. A two-part exploration of the integral covers measurable functions, convergence theorems, convergence in mean, Fourier theory, and other topics. A chapter on calculus examines change of variables, differentiation of integrals, and integration of derivatives and by parts. The text concludes with a consideration of more general measures, including absolute continuity and convolution products.
Reprint of the Holt, Rinehart & Winston, New York, 1962 edition.
mathematics, calculus, math majors, advanced math, undergraduate students, real variable theory, helpful exercises, sets and functions, measurable sets, sets of measure zero, borel sets, nonmeasurable sets, integrals, convergence theorems, convergence in mean, fourier theory, change of variables, differentiation, derivatives, general measures, continuity, convolution, young frechet approach, fubinis theorems, complex and vector functions, approximations to integrable functions, integration;Lebesgue Integration; Lebesgue Measure; Fourier Theory; Borel Measures; Fourier Transforms
