Suchen und Finden
Nonmeasurable Sets and Functions
von: Alexander Kharazishvili
Elsevier Trade Monographs, 2004
ISBN: 9780080479767 , 349 Seiten
Format: PDF, ePUB, OL
Kopierschutz: DRM
Preis: 137,00 EUR
Cover
1
Contents
5
Preface
7
Chapter 1. The Vitali Theorem
13
Theorem 1
14
Theorem 2
15
Theorem 3
18
Theorem 4
18
Theorem 5
20
Theorem 6
22
Exercises
24
Chapter 2. The Bernstein Construction
29
Theorem 1
31
Theorem 2
33
Theorem 3
34
Theorem 4
36
Theorem 5
37
Exercises
39
Chapter 3. Nonmeasurable Sets Associated with Hamel Bases
47
Theorem 1
47
Theorem 2
48
Lemma 1
49
Lemma 2
50
Theorem 3
50
Theorem 4
51
Theorem 5
52
Theorem 6
59
Theorem 7
61
Exercises
62
Chapter 4. The Fubini Theorem and Nonmeasurable Sets
68
Theorem 1
75
Lemma 1
77
Lemma 2
80
Theorem 2
81
Theorem 3
84
Theorem 4
85
Exercises
87
Chapter 5. Small Nonmeasurable Sets
91
Theorem 1
92
Theorem 2
93
Theorem 3
94
Theorem 4
96
Lemma 1
99
Lemma 2
101
Theorem 5
102
Exercises
105
Chapter 6. Strange Subsets of the Euclidean Plane
114
Theorem 1
115
Lemma 1
117
Theorem 2
118
Theorem 3
119
Lemma 2
123
Lemma 3
123
Lemma 4
126
Theorem 4
127
Exercises
127
Chapter 7. Some Special Constructions of Nonmeasurable Sets
133
Theorem 1
134
Theorem 2
139
Lemma 1
147
Theorem 3
148
Exercises
149
Chapter 8. The Generalized Vitali Construction
157
Lemma 1
159
Lemma 2
160
Lemma 3
161
Lemma 4
163
Lemma 5
164
Theorem 1
165
Theorem 2
169
Exercises
174
Chapter 9. Selectors Associated with Countable Subgroups
175
Lemma 1
179
Lemma 2
179
Lemma 3
180
Lemma 4
180
Lemma 5
181
Lemma 6
181
Lemma 7
181
Theorem 1
183
Theorem 2
184
Theorem 3
185
Exercises
186
Chapter 10. Selectors Associated with Uncountable Subgroups
191
Theorem 1
194
Theorem 2
197
Theorem 3
198
Exercises
203
Chapter 11. Absolutely Nonmeasurable Sets in Groups
207
Lemma 1
208
Lemma 2
215
Lemma 3
216
Theorem 1
220
Lemma 4
222
Lemma 5.
223
Theorem 2
224
Theorem 3
225
Theorem 4
225
Theorem 5
225
Theorem 6
226
Theorem 7
227
Exercises
228
Chapter 12. Ideals Producing Nonmeasurable Unions of Sets
232
Lemma 1
234
Theorem 1
235
Theorem 2
237
Theorem 3
237
Theorem 4
238
Lemma 2
239
Lemma 3
240
Lemma 4
240
Lemma 5
242
Theorem 5
243
Theorem 6
243
Theorem 7
243
Theorem 8
244
Theorem 9
244
Exercises
245
Chapter 13. Measurability Properties of Subgroups of a Given Group
248
Lemma 1
249
Lemma 2
251
Lemma 3
251
Theorem 1
253
Theorem 2
254
Theorem 3
257
Lemma 4
259
Lemma 5
261
Lemma 6
262
Lemma 7
264
Lemma 8
264
Theorem 4
265
Exercises
267
Chapter 14. Groups of Rotations and Nonmeasurable Sets
271
Lemma 1
278
Lemma 2
279
Lemma 3
279
Lemma 4
279
Theorem 1
280
Theorem 2
281
Exercises
283
Chapter 15. Nonmeasurable Sets Associated with Filters
288
Lemma 1
290
Lemma 2
292
Theorem 1
294
Lemma 3
295
Lemma 4
297
Lemma 5
299
Theorem 2
300
Exercises
302
Appendix 1 Logical Aspects of the Existence of Nonmeasurable Sets
306
Theorem 1
314
Theorem 2
316
Appendix 2 Some Facts From the Theory of Commutative Groups
320
Theorem 1
322
Theorem 2
324
Theorem 3
327
Theorem 4
327
Bibliography
329
Subject Index
346
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