دانلود کتاب A Primer of Real Functions

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Front Cover......Page 1
A Primer of Real Functions......Page 5
Copyright Page......Page 4
Preface to the Fourth Edition......Page 9
Preface to the Third Edition......Page 11
Contents......Page 15
1 Sets......Page 17
2 Sets of real numbers......Page 21
3 Countable and uncountable sets......Page 24
4 Metric spaces......Page 37
5 Open and closed sets......Page 41
6 Dense and nowhere dense sets......Page 54
7 Compactness......Page 61
8 Convergence and completeness......Page 68
9 Nested sets and Baire\'s theorem......Page 77
10 Some applications of Baire\'s Theorem......Page 82
11 Sets of measure zero......Page 89
12 Functions......Page 93
13 Continuous functions......Page 99
14 Properties of continuous functions......Page 106
15 Upper and lower limits......Page 121
16 Sequences of functions......Page 124
17 Uniform convergence......Page 128
18 Pointwise limits of continuous functions......Page 139
19 Approximations to continuous functions......Page 142
20 Linear functions......Page 148
21 Derivatives......Page 155
22 Monotonic functions......Page 174
23 Convex functions......Page 191
24 Infinitely differentiable functions......Page 202
25 Lebesgue measure......Page 211
26 Measurable functions......Page 217
27 Definition of the Lebesgue integral......Page 222
28 Properties of Lebesgue integrals......Page 227
29 Applications of the Lebesgue integral......Page 233
30 Stieltjes integrals......Page 240
31 Applications of the Stieltjes integral......Page 245
32 Partial sums of infinite series......Page 253
Answers to Exercises......Page 261
Index......Page 297
Back Cover......Page 323