Measure, Integral and Probability:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2004
|
| Edition: | 2. ed. |
| Series: | Springer Undergraduate Mathematics Series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | 311 S. Ill. |
| ISBN: | 1852337818 |
Staff View
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Record in the Search Index
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MAREK CAPINSKI AND EKKEHARD KOPP MEASURE, INTEGRAL AND PROBABILITY
SECOND EDITION WITH 23 FIGURES 4Q SPRINGER CONTENTS 1. MOTIVATION AND
PRELIMINARIES 1 1.1 NOTATION AND BASIC SET THEORY 2 1.1.1 SETS AND
FUNCTIONS 2 1.1.2 COUNTABLE AND UNCOUNTABLE SETS IN R 4 1.1.3
TOPOLOGICAL PROPERTIES OF SETS IN R 5 1.2 THE RIEMANN INTEGRAL: SCOPE
AND LIMITATIONS 7 1.3 CHOOSING NUMBERS AT RANDOM 12 2. MEASURE 15 2.1
NULL SETS 15 2.2 OUTER MEASURE 20 2.3 LEBESGUE-MEASURABLE SETS AND
LEBESGUE MEASURE 26 2.4 BASIC PROPERTIES OF LEBESGUE MEASURE 35 2.5
BOREL SETS 40 2.6 PROBABILITY 45 2.6.1 PROBABILITY SPACE 46 2.6.2
EVENTS: CONDITIONING AND INDEPENDENCE \ 46 2.6.3 APPLICATIONS TO
MATHEMATICAL FINANCE 49 2.7 PROOFS OF PROPOSITIONS 51 3. MEASURABLE
FUNCTIONS 55 3.1 THE EXTENDED REAL LINE 55 3.2 LEBESGUE-MEASURABLE
FUNCTIONS 55 3.3 EXAMPLES 59 3.4 PROPERTIES 60 3.5 PROBABILITY 66 XIV
CONTENTS 3.5.1 RANDOM VARIABLES 66 3.5.2 (T-FIELDS GENERATED BY RANDOM
VARIABLES 67 3.5.3 PROBABILITY DISTRIBUTIONS 68 3.5.4 INDEPENDENCE OF
RANDOM VARIABLES 70 3.5.5 APPLICATIONS TO MATHEMATICAL FINANCE 70 3.6
PROOFS OF PROPOSITIONS 73 4. INTEGRAL 75 4.1 DEFINITION OF THE INTEGRAL
75 4.2 MONOTONE CONVERGENCE THEOREMS 82 4.3 INTEGRABLE FUNCTIONS 86 4.4
THE DOMINATED CONVERGENCE THEOREM 92 4.5 RELATION TO THE RIEMANN
INTEGRAL 97 4.6 APPROXIMATION OF MEASURABLE FUNCTIONS 102 4.7
PROBABILITY 105 4.7.1 INTEGRATION WITH RESPECT TO PROBABILITY
DISTRIBUTIONS . 105 4.7.2 ABSOLUTELY CONTINUOUS MEASURES: EXAMPLES OF
DENSITIES 107 4.7.3 EXPECTATION OF A RANDOM VARIABLE 114 4.7.4
CHARACTERISTIC FUNCTION 115 4.7.5 APPLICATIONS TO MATHEMATICAL FINANCE
117 4.8 PROOFS OF PROPOSITIONS 119 5. SPACES OF INTEGRABLE FUNCTIONS 125
5.1 THE SPACE L 1 126 5.2 THE HILBERT SPACE L 2 131 5.2.1 PROPERTIES OF
THE L 2 -NORM 132 5.2.2 INNER PRODUCT SPACES 135 5.2.3 ORTHOGONALITY AND
PROJECTIONS 137 5.3 THE IP SPACES: COMPLETENESS 140 5.4 PROBABILITY 146
5.4.1 MOMENTS 146 5.4.2 INDEPENDENCE 150 5.4.3 CONDITIONAL EXPECTATION
(FIRST CONSTRUCTION) 153 5.5 PROOFS OF PROPOSITIONS 155 6. PRODUCT
MEASURES 159 6.1 MULTI-DIMENSIONAL LEBESGUE MEASURE 159 6.2 PRODUCT
A-FIELDS 160 6.3 CONSTRUCTION OF THE PRODUCT MEASURE 162 6.4 FUBINI'S
THEOREM 169 6.5 PROBABILITY 173 CONTENTS XV 6.5.1 JOINT DISTRIBUTIONS
173 6.5.2 INDEPENDENCE AGAIN 175 6.5.3 CONDITIONAL PROBABILITY 177 6.5.4
CHARACTERISTIC FUNCTIONS DETERMINE DISTRIBUTIONS 180 6.5.5 APPLICATION
TO MATHEMATICAL FINANCE 182 6.6 PROOFS OF PROPOSITIONS 185 7. THE
RADON-NIKODYM THEOREM 187 7.1 DENSITIES AND CONDITIONING 187 7.2 THE
RADON-NIKODYM THEOREM 188 7.3 LEBESGUE-STIELTJES MEASURES 199 7.3.1
CONSTRUCTION OF LEBESGUE-STIELTJES MEASURES 199 7.3.2 ABSOLUTE
CONTINUITY OF FUNCTIONS 204 7.3.3 TUNCTIONS OF BOUNDED VARIATION 206
7.3.4 SIGNED MEASURES 210 7.3.5 HAHN-JORDAN DECOMPOSITION 216 7.4
PROBABILITY 218 7.4.1 CONDITIONAL EXPECTATION RELATIVE TO A CR-FIELD 218
7.4.2 MARTINGALES 222 7.4.3 DOOB DECOMPOSITION 226 7.4.4 APPLICATIONS TO
MATHEMATICAL FINANCE 232 7.5 PROOFS OF PROPOSITIONS 235 8. LIMIT
THEOREMS 241 8.1 MODES OF CONVERGENCE 241 8.2 PROBABILITY 243 8.2.1
CONVERGENCE IN PROBABILITY 245 8.2.2 WEAK LAW OF LARGE NUMBERS 249 8.2.3
THE BOREL-CANTELLI LEMMAS 255 8.2.4 STRONG LAW OF LARGE NUMBERS 260
8.2.5 WEAK CONVERGENCE 268 8.2.6 CENTRAL LIMIT THEOREM 273 8.2.7
APPLICATIONS TO MATHEMATICAL FINANCE 280 8.3 PROOFS OF PROPOSITIONS 283
SOLUTIONS 287 APPENDIX 301 REFERENCES 305 INDEX 307 |
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| author | Capiński, Marek 1951- Kopp, Peter E. 1944- |
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| author_role | aut aut |
| author_sort | Capiński, Marek 1951- |
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| ctrlnum | (OCoLC)611448791 (DE-599)BVBBV019339102 |
| dewey-full | 515/.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.42 |
| dewey-search | 515/.42 |
| dewey-sort | 3515 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
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| indexdate | 2025-03-28T17:07:56Z |
| institution | BVB |
| isbn | 1852337818 |
| language | English |
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| physical | 311 S. Ill. |
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| spelling | Capiński, Marek 1951- Verfasser (DE-588)172897866 aut Measure, Integral and Probability Marek Capinski and Ekkehard Kopp 2. ed. London [u.a.] Springer 2004 311 S. Ill. txt rdacontent n rdamedia nc rdacarrier Springer Undergraduate Mathematics Series Hier auch später erschienene, unveränderte Nachdrucke Intégrales généralisées Mesure, Théorie de la Probabilidade larpcal Probabilités Integrals, Generalized Measure theory Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Lebesgue-Integral (DE-588)4034949-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s DE-604 Lebesgue-Integral (DE-588)4034949-4 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Kopp, Peter E. 1944- Verfasser (DE-588)120339889 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012803734&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Capiński, Marek 1951- Kopp, Peter E. 1944- Measure, Integral and Probability Intégrales généralisées Mesure, Théorie de la Probabilidade larpcal Probabilités Integrals, Generalized Measure theory Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Maßtheorie (DE-588)4074626-4 gnd Lebesgue-Integral (DE-588)4034949-4 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4074626-4 (DE-588)4034949-4 |
| title | Measure, Integral and Probability |
| title_auth | Measure, Integral and Probability |
| title_exact_search | Measure, Integral and Probability |
| title_full | Measure, Integral and Probability Marek Capinski and Ekkehard Kopp |
| title_fullStr | Measure, Integral and Probability Marek Capinski and Ekkehard Kopp |
| title_full_unstemmed | Measure, Integral and Probability Marek Capinski and Ekkehard Kopp |
| title_short | Measure, Integral and Probability |
| title_sort | measure integral and probability |
| topic | Intégrales généralisées Mesure, Théorie de la Probabilidade larpcal Probabilités Integrals, Generalized Measure theory Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Maßtheorie (DE-588)4074626-4 gnd Lebesgue-Integral (DE-588)4034949-4 gnd |
| topic_facet | Intégrales généralisées Mesure, Théorie de la Probabilidade Probabilités Integrals, Generalized Measure theory Probabilities Wahrscheinlichkeitstheorie Maßtheorie Lebesgue-Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012803734&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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