Null additive set functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Bratislava
Ister Science [u.a.]
1995
|
| Schriftenreihe: | Mathematics and its applications
337 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 315 S. |
| ISBN: | 8088683122 0792336585 9789048146024 |
Internformat
MARC
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| 245 | 1 | 0 | |a Null additive set functions |c by Endre Pap |
| 264 | 1 | |a Bratislava |b Ister Science [u.a.] |c 1995 | |
| 300 | |a XII, 315 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 337 | |
| 650 | 7 | |a Fonctions d'ensemble |2 ram | |
| 650 | 4 | |a Set functions | |
| 650 | 0 | 7 | |a Monoton wachsende Mengenfunktion |0 (DE-588)4369572-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Monoton wachsende Mengenfunktion |0 (DE-588)4369572-3 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-007048396 | ||
Datensatz im Suchindex
| _version_ | 1804125042012848128 |
|---|---|
| adam_text | Contents
Preface ix
List of Symbols xi
1 Introduction 1
1.1 Non Additive Set Functions 1
1.2 The Concept of the Book 3
1.3 Notes and References 6
2 General Properties 7
2.1 Basic Definitions 7
2.1.1 Preliminaries 7
2.1.2 Null Additive Set Functions 12
2.2 Important Classes of Set Functions 16
2.2.1 Triangular Conorm Decomposable Measures 16
2.2.2 Pseudo Addition Decomposable Measures 21
2.2.3 The Maxitive Measure 22
2.2.4 Fractals, Hausdorff Measure and Dimension 25
2.2.5 Fuzzy Measures 27
2.2.6 Submeasures 27
2.2.7 Belief Measure and Plausibility Measure 29
2.2.8 fc Triangular Set Functions 31
2.2.9 Distorted Measures 32
2.2.10 Capacities 33
2.2.11 Approximately Additive Set Functions 35
2.3 Notes and References 36
3 Variations 37
3.1 Disjoint Variation 37
3.2 The Chain Variation 46
3.3 The Space BV 49
3.4 Notes and References 54
4 Additive Representations of Set Function 55
4.1 Finite Case 55
4.2 General Case 58
4.3 The Space CV 61
vj CONTENTS
4.4 Interpreters 63
4.5 Notes and References 66
5 Autocontinuity of Set Functions 67
5.1 Autocontinuities 67
5.1.1 Basic Properties 67
5.1.2 Examples 71
5.1.3 Countable Case 74
5.2 Submeasures and Frechet Nikodym Topologies 77
5.2.1 Topological Ring 77
5.2.2 Topology Induced by Submeasures 79
5.2.3 Non negative Monotone Set Functions 82
5.3 Extensions 83
5.4 Linearly Indexed Families of Submeasures 90
5.4.1 The Modular space 90
5.4.2 Lebesgue Dominated Convergence Type Theorem 92
5.4.3 Monotone Type Sequence of Functions 93
5.4.4 Matrix Transformation 93
5.4.5 Functions of Monotone Type 96
5.4.6 p Modulus of Continuity 97
5.4.7 Application to Approximation Theory 100
5.5 Notes and References 104
6 Decompositions of Set Functions 105
6.1 Hahn Decomposition Theorem 105
6.1.1 Signed Fuzzy Measures 105
6.1.2 Hahn Decomposition 107
62 Jordan Decomposition Theorem Ill
6.3 Lebesgue Decomposition Theorem 114
6.3.1 Null Additive Set Functions 114
6.3.2 cr Null Additive Set Functions 117
6.4 Atoms of Null Additive Set Functions 121
6.5 Saks Decomposition Theorem 127
6.6 Hewitt Yosida Decomposition Theorem 129
6.6.1 Lattice with Relative Complement 130
6.6.2 D Decomposable Measures 132
6.6.3 Hewitt Yosida Decomposition 134
6.7 Notes and References 137
7 Choquet and Sugeno Integrals 139
7.1 Measurable Functions 139
7.1.1 Measurability 139
7.1.2 s NulI Sets 141
7.1.3 Egoroff s and Riesz Theorems 143
7.2 Choquet Integral for Non Negative Case 148
7.3 Symmetric Choquet (Sipos) integral 152
7.4 Convergence Theorems for Symmetric Choquet (Sipos) Integral 162
7.5 The Submodular Theorem 167
7.6 Asymmetric Choquet Integral 176
7.7 Sugeno Integral ]79
CONTENTS vjj
7.8 Set Functions Defined by Sugeno Integrals 187
7.9 Comparison of Choquet and Sugeno Integrals 189
7.10 Notes and References 190
8 Integrals Based on Decomposable Measures 192
8.1 Pseudo Integral 192
8.2 Some Other Types of Integrals 199
8.2.1 Weber Integral 199
8.2.2 Murofushi Sugeno Integral 201
8.3 g Calculus 204
8.4 Applications of (/ Calculus to Nonlinear
Differential Equations 209
8.4.1 Ordinary Differential equations 209
8.4.2 The Burgers equation 213
8.5 Applications of the Pseudo integral on Nonlinear
Difference Equations 213
8.6 Notes and References 218
9 The Range and Regularity of Null Additive Set Function 219
9.1 The Range of Autocontinuous Set Function 219
9.1.1 Darboux property 219
9.1.2 Lyapunov s Type Theorems 221
9.2 Regular Set Functions 224
9.3 Notes and References 230
10 Radon Nikodym Type Theorems and Representation Theorems . 231
10.1 Radon Nikodym Theorem for the Choquet Integral 231
10.1.1 The Finite Case 231
10.1.2 The Chain Condition 233
10.2 Representation of the Choquet Integral 235
10.2.1 Min Minus Min Representation 235
10.2.2 Mean of Mins and Min of Means Representation 236
10.3 Radon Nikodym Theorem for Sugeno Integral 239
10.4 Daniell Greco Stone Representation of Functionals 240
10.4.1 Outer Set Function 241
10.4.2 Non Linear Functionals 242
10.4.3 The Representation 243
10.5 Notes and References 246
11 fc Triangular Set Functions 247
11.1 Diagonal Theorem for Triangular Set Function 247
11.2 Diagonal Theorems and Some of Their Applications 250
11.2.1 Diagonal Theorems 250
11.2.2 Some Applications 252
11.2.3 The Adjoint Theorem 256
11.2.4 The Fatness Condition 259
11.3 The Brooks Jewett Type Theorem 261
11.3.1 Algebras with Some Additional Properties 261
11.3.2 Convergence Theorem 262
11.4 Brooks Jewett Theorem on Orthomodular Lattice 266
vJjj CONTENTS
11.4.1 Orthomodular Lattice 266
11.4.2 fc Triangular Function 269
11.5 Dieudonne Type Theorems 275
11.5.1 Real ^ Triangular Set Functions 275
11.5.2 Semigroup Valued fc Triangular Set Functions 280
11.5.3 Convergence Theorem 281
11.6 Notes and References 282
12 Convergence and Boundedness Theorems on Difference Poset ... 284
12.1 Difference Posets 284
12.1.1 Definitions and Examples 284
12.1.2 © orthogonality 288
12.2 Nikodym Boundedness Theorem 289
12.2.1 Boundedness in Uniform Space 289
12.2.2 Boundedness Theorem 290
12.3 Convergence Theorem 295
12.4 Notes and References 298
Bibliography 299
Index 313
|
| any_adam_object | 1 |
| author | Pap, Endre |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.4 |
| dewey-search | 515/.4 |
| dewey-sort | 3515 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010573492 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:55:16Z |
| institution | BVB |
| isbn | 8088683122 0792336585 9789048146024 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007048396 |
| oclc_num | 32855579 |
| open_access_boolean | |
| owner | DE-12 DE-739 DE-29T |
| owner_facet | DE-12 DE-739 DE-29T |
| physical | XII, 315 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Ister Science [u.a.] |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Pap, Endre Verfasser (DE-588)125398549 aut Null additive set functions by Endre Pap Bratislava Ister Science [u.a.] 1995 XII, 315 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 337 Fonctions d'ensemble ram Set functions Monoton wachsende Mengenfunktion (DE-588)4369572-3 gnd rswk-swf Monoton wachsende Mengenfunktion (DE-588)4369572-3 s DE-604 Mathematics and its applications 337 (DE-604)BV008163334 337 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007048396&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pap, Endre Null additive set functions Mathematics and its applications Fonctions d'ensemble ram Set functions Monoton wachsende Mengenfunktion (DE-588)4369572-3 gnd |
| subject_GND | (DE-588)4369572-3 |
| title | Null additive set functions |
| title_auth | Null additive set functions |
| title_exact_search | Null additive set functions |
| title_full | Null additive set functions by Endre Pap |
| title_fullStr | Null additive set functions by Endre Pap |
| title_full_unstemmed | Null additive set functions by Endre Pap |
| title_short | Null additive set functions |
| title_sort | null additive set functions |
| topic | Fonctions d'ensemble ram Set functions Monoton wachsende Mengenfunktion (DE-588)4369572-3 gnd |
| topic_facet | Fonctions d'ensemble Set functions Monoton wachsende Mengenfunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007048396&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT papendre nulladditivesetfunctions |