- Category: Computer
- Author: Terrence Tao
- Pages: 206 pages
- File type: Author’s Preliminary Version, PDF (265 pages, 1.3 MB)
Read and download free eBook intituled An Introduction to Measure Theory in format Author’s Preliminary Version, PDF (265 pages, 1.3 MB) – 206 pages created by Terrence Tao.
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis.
The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini’s theorem, and the Caratheodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory.
The material is intended to cover a quarter or semester’s worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former.
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