Null-additive set functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer [u.a.]
1995
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| Series: | Mathematics and its applications
337 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 315 S. |
| ISBN: | 0792336585 8088683122 |
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MARC
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Record in the Search Index
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| adam_text | NULL-ADDITIVE SET FUNCTIONS BY ENDRE PAP INSTITUTE OF MATHEMATICS,
UNIVERSITY OFNOVI SAD, NOVI SAD, YUGOSLAVIA ISTER SCIENCE BRATISLAVA
KLUWER ACADEMIC PUBLISHERS DORDRECHT * BOSTON * LONDON 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
IT-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 4 9 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 VI 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 TOPOLOGICAI RING 77 5.2.2 TOPOLOGY INDUCED BY SUBMEASUTES 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 6.2 JORDAN
DECOMPOSITION THEOREM ILL 6.3 LEBESGUE DECOMPOSITION THEOREM 114 6.3.1
NULL-ADDITIVE SET FUNCTIONS 114 6.3.2 (T-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-NULL-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 179 CONTENTS VLL
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 3-CALCULUS 204 8.4 APPLICATIONS OF
G-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 FE-TRIANGULAR SET FUNCTIONS 247 11.1 DIAGONAL THEOREM
FOR TRIANGULAR SET FUNCTION 247 11.2 DIAGONAL THEOREMS AND SEME 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 VM CONTENTS 11.4.1
ORTHOMODULAR LATTICE 266 11.4.2 FC-TRIANGULAR FUNCTION 269 11.5
DIEUDONNE TYPE THEOREMS 275 11.5.1 REAL FC-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 |
| author_facet | Pap, Endre |
| author_role | aut |
| author_sort | Pap, Endre |
| author_variant | e p ep |
| building | Verbundindex |
| bvnumber | BV024974826 |
| classification_rvk | SK 430 |
| ctrlnum | (OCoLC)832501019 (DE-599)BVBBV024974826 |
| dewey-full | 515.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.4 |
| dewey-search | 515.4 |
| dewey-sort | 3515.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV024974826 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:24:52Z |
| institution | BVB |
| isbn | 0792336585 8088683122 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019642341 |
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| physical | XII, 315 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Kluwer [u.a.] |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Pap, Endre Verfasser aut Null-additive set functions by Endre Pap Dordrecht [u.a.] Kluwer [u.a.] 1995 XII, 315 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 337 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 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019642341&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pap, Endre Null-additive set functions Mathematics and its applications 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 | Monoton wachsende Mengenfunktion (DE-588)4369572-3 gnd |
| topic_facet | Monoton wachsende Mengenfunktion |
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