A Second Course on Real Functions

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CUP Archive, Mar 25, 1982 - Mathematics - 200 pages
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When considering a mathematical theorem one ought not only to know how to prove it but also why and whether any given conditions are necessary. All too often little attention is paid to to this side of the theory and in writing this account of the theory of real functions the authors hope to rectify matters. They have put the classical theory of real functions in a modern setting and in so doing have made the mathematical reasoning rigorous and explored the theory in much greater depth than is customary. The subject matter is essentially the same as that of ordinary calculus course and the techniques used are elementary (no topology, measure theory or functional analysis). Thus anyone who is acquainted with elementary calculus and wishes to deepen their knowledge should read this.
 

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Contents

Introduction
1
Monotone functions
9
Subsets of R
35
Continuity
52
Differentiation
78
Borel measurability
102
Integration
130
a characterization of
189
Further reading
196
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