an the limitations of the Riemann integral be overcome? What is its relationship with modern analysis?
The theory of Lebesgue integration is a crucial component in the development of modern analysis. This book is an in-depth real analysis textbook, which introduces the basic theory of modern analysis and the basic skills of analysis. Based on the knowledge of real analysis, the theory of interpolation of operators and the Fourier transform theory are further introduced systematically. The main contents include: abstract measures and integrals, measure and topology, Lebesgue integration on Rn, the interpolation of operators on Lp(Rn), Hardy-Littlewood maximal function, convolution and the Fourier transform. They play an important role in harmonic analysis, partial differential equations, probability and numerical analysis. This book is moderately difficult and detailed, focusing on the combination of abstract and concrete, and training readers to skillfully use modern analysis.
This textbook is an excellent reference book for readers studying the fields of Harmonic analysis and partial differential equations. It is intended for advanced undergraduate and graduate students in university mathematics, as well as mathematicians and physicists in general.
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Contents:
Abstract Measure and Integral
Measure and Topology
Lebesgue Integration on ℝn
The Interpolation of Operator on Lp(ℝn)
Hardy–Littlewood Maximal Function
Convolution
The Fourier Transform
Readership: Advanced undergraduate and graduate students, mathematicians and physicists.
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Introduction to the Basics of Real Analysis
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Contents:
Sets and Functions
Real Number System
Basics of Real Analysis
Sequences of Real Numbers
Limits and Continuity
Uniform Continuity of Real Functions
Differentiability of Real Functions
Uniform Convergence of Sequences and Series of Real Functions
Functions of Several Variables
Riemann Integration
The Improper Integrals
Metric Spaces
原價:
3390
售價:
3221
現省:
169元
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