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Derivation and Integration

Washek F. Pfeffer
Format
Book
Published
Cambridge, UK ; New York : Cambridge University Press, 2001.
Language
English
Series
Cambridge Tracts in Mathematics
ISBN
0521792681
Contents
  • 1.2. Topology 4
  • 1.3. Measures 11
  • 1.4. Covering theorems 16
  • 1.5. Densities 21
  • 1.6. Lipschitz maps 27
  • 1.7. BV functions 29
  • 1.8. BV sets 34
  • 1.9. Slices of BV sets 39
  • 1.10. Approximating BV sets 42
  • 2. Charges 47
  • 2.1. Definition and examples 47
  • 2.2. Spaces of charges 57
  • 2.3. Derivates 60
  • 2.4. Derivability 67
  • 2.5. Reduced charges 76
  • 2.6 Partitions 82
  • 3. Variations of charges 90
  • 3.1. Some classical concepts 90
  • 3.2. Essential variation 97
  • 3.3. Integration problem 106
  • 3.4. An excursion to Hausdorff measures 109
  • 3.5. Critical variation 118
  • 3.6. AC[subscript *] charges 124
  • 3.7. Essentially clopen sets 130
  • 4. Charges and BV functions 135
  • 4.1. Charge F x L[superscript 1] 135
  • 4.2. Space (CH[subscript *](E),S) 142
  • 4.3. Duality 148
  • 4.4. More on BV functions 154
  • 4.5. Charge F [angle] g 162
  • 4.6. Lipeomorphisms 173
  • 5. Integration 186
  • 5.1. R-integral 186
  • 5.2. Multipliers 192
  • 5.3. Change of variables 197
  • 5.4. Averaging 205
  • 5.5. Riemann approach 209
  • 5.6. Charges as distributional derivatives 217
  • 5.7. Lebesgue integral 223
  • 6. Extending the integral 229
  • 6.1. Buczolich's example 229
  • 6.2. I-convergence 236
  • 6.3. GR-integral 240
  • 6.4. Additional properties 246.
Description
xvi, 266 p. ; 24 cm.
Notes
Includes bibliographical references (p. 255-258) and index.
Series Statement
Cambridge tracts in mathematics 140
Technical Details
  • Access in Virgo Classic
  • Staff View

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    g| 1.2. t| Topology g| 4 -- g| 1.3. t| Measures g| 11 -- g| 1.4. t| Covering theorems g| 16 -- g| 1.5. t| Densities g| 21 -- g| 1.6. t| Lipschitz maps g| 27 -- g| 1.7. t| BV functions g| 29 -- g| 1.8. t| BV sets g| 34 -- g| 1.9. t| Slices of BV sets g| 39 -- g| 1.10. t| Approximating BV sets g| 42 -- g| 2. t| Charges g| 47 -- g| 2.1. t| Definition and examples g| 47 -- g| 2.2. t| Spaces of charges g| 57 -- g| 2.3. t| Derivates g| 60 -- g| 2.4. t| Derivability g| 67 -- g| 2.5. t| Reduced charges g| 76 -- g| 2.6 t| Partitions g| 82 -- g| 3. t| Variations of charges g| 90 -- g| 3.1. t| Some classical concepts g| 90 -- g| 3.2. t| Essential variation g| 97 -- g| 3.3. t| Integration problem g| 106 -- g| 3.4. t| An excursion to Hausdorff measures g| 109 -- g| 3.5. t| Critical variation g| 118 -- g| 3.6. t| AC[subscript *] charges g| 124 -- g| 3.7. t| Essentially clopen sets g| 130 -- g| 4. t| Charges and BV functions g| 135 -- g| 4.1. t| Charge F x L[superscript 1] g| 135 -- g| 4.2. t| Space (CH[subscript *](E),S) g| 142 -- g| 4.3. t| Duality g| 148 -- g| 4.4. t| More on BV functions g| 154 -- g| 4.5. t| Charge F [angle] g g| 162 -- g| 4.6. t| Lipeomorphisms g| 173 -- g| 5. t| Integration g| 186 -- g| 5.1. t| R-integral g| 186 -- g| 5.2. t| Multipliers g| 192 -- g| 5.3. t| Change of variables g| 197 -- g| 5.4. t| Averaging g| 205 -- g| 5.5. t| Riemann approach g| 209 -- g| 5.6. t| Charges as distributional derivatives g| 217 -- g| 5.7. t| Lebesgue integral g| 223 -- g| 6. t| Extending the integral g| 229 -- g| 6.1. t| Buczolich's example g| 229 -- g| 6.2. t| I-convergence g| 236 -- g| 6.3. t| GR-integral g| 240 -- g| 6.4. t| Additional properties g| 246.
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