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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis
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A (Terse) Introduction to Lebesgue Integration (Paperback)
Loot Price: R1,530
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A (Terse) Introduction to Lebesgue Integration (Paperback)
Series: Student Mathematical Library
Expected to ship within 12 - 17 working days
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This book provides a student's first encounter with the concepts of
measure theory and functional analysis. Its structure and content
reflect the belief that difficult concepts should be introduced in
their simplest and most concrete forms. Despite the use of the word
'terse' in the title, this text might also have been called ""A
(Gentle) Introduction to Lebesgue Integration"". It is terse in the
sense that it treats only a subset of those concepts typically
found in a substantial graduate-level analysis course. The book
emphasizes the motivation of these concepts and attempts to treat
them simply and concretely. In particular, little mention is made
of general measures other than Lebesgue until the final chapter and
attention is limited to R as opposed to Rn. After establishing the
primary ideas and results, the text moves on to some applications.
Chapter 6 discusses classical real and complex Fourier series for
L2 functions on the interval and shows that the Fourier series of
an L2 function converges in L2 to that function. Chapter 7
introduces some concepts from measurable dynamics. The Birkhoff
ergodic theorem is stated without proof and results on Fourier
series from chapter 6 are used to prove that an irrational rotation
of the circle is ergodic and that the squaring map on the complex
numbers of modulus 1 is ergodic. This book is suitable for an
advanced undergraduate course or for the start of a graduate
course. The text presupposes that the student has had a standard
undergraduate course in real analysis.
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