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An Introduction to Measure Theory (Paperback)
Loot Price: R2,253
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An Introduction to Measure Theory (Paperback)
Series: Graduate Studies in Mathematics
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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. The central role of key
principles (such as Littlewood's three principles) as providing
guiding intuition to the subject is also emphasized. There are a
large number of exercises throughout that develop key aspects of
the theory, and are thus an integral component of the text. As a
supplementary section, a discussion of general problem-solving
strategies in analysis is also given. The last three sections
discuss optional topics related to the main matter of the book.
General
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