Interpretations of probability:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
de Gruyter
2009
|
| Ausgabe: | 2., rev. and extended ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 205 - 214 |
| Beschreibung: | XX, 217 S. 25 cm |
| ISBN: | 9783110207484 |
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| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 2009 | |
| 300 | |a XX, 217 S. |c 25 cm | ||
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Datensatz im Suchindex
| _version_ | 1805092247225499648 |
|---|---|
| adam_text |
CONTENTS 1 FOUNDATIONS OF PROBABILITY THEORY 1 1 A FEW WORDS ABOUT
MEASURES 1 2 CLASSICAL AND ENSEMBLE DEFINITIONS OF PROBABILITY 1 2.1
CLASSICAL DEFINITIONOF PROBABILITY 1 2.2 ENSEMBLE (PROPORTIONAL)
DEFINITION OF PROBABILITY 2 3 FREQUENCY THEORY OF PROBABILITY 4 4
KOLMOGOROV'S MEASURE-THEORETICAL THEORY 8 5 KOLMOGOROV'S IDEAS ON
PROBABILITY 10 6 MEASURE-THEORETICAL APPROACH AND INTERPRETATIONSOF
PROBABILITY 16 6.1 ENSEMBLE-FREQUENCY INTERPRETATION 16 6.2
MEASURE-THEORETICAL APPROACH AND THE ENSEMBLE INTERPRETATION . . 17 6.3
MEASURE-THEORETICAL APPROACH AND FREQUENCY PROBABILITY 17 6.4
MEASURE-THEORETICAL APPROACH AND ENSEMBLE-FREQUENCY INTERPRE- TATION 18
7 SUBJECTIVE (BAYESIAN) PROBABILITY THEORY 21 8 FOUNDATIONS OFRANDOMNESS
23 8.1 EXISTENCE OF COLLECTIVES; KAMKE'S OBJECTION 23 8.2 GEOMETRIE AND
FREQUENCY SPACES 26 8.3 VILLE'S OBJECTION 26 8.4 ENSEMBLE PROBABILITY
APPROACH TO RANDOMNESS 27 8.5 KOLMOGOROV COMPLEXITY 27 9 OPERATION OF
COMBINING OF COLLECTIVES 29 10 INDEPENDENCE OF COLLECTIVES 32 11
FREQUENCY AND MEASURE - THEORETICAL VIEWPOINTS ON INDEPENDENCE . 33 12
GENERALIZATIONOF THE OPERATION OF COMBINING . 35 13 COMPARATIVE
PROBABILITY 35 2 QUANTUM PROBABILITIES 37 1 CLASSICAL AND QUANTUM
PROBABILITY RULES 37 1.1 PROPERTIESOF PHYSICAL SYSTEMS 37 1.2 REALISM 37
1.3 EMPIRICISM 38 1. BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/991725050 DIGITALISIERT DURCH XVIII CONTENTS 2
INTERPRETATION OF WAVE FUNCTION 42 2.1 ENSEMBLE REALIST INTERPRETATION -
EINSTEINIAN INTERPRETATION . . . . 42 2.2 INDIVIDUAL REALISTS
INTERPRETATION - 'LENINGRAD INTERPRETATION' . . . 43 2.3 ENSEMBLE
EMPIRICISTS INTERPRETATION - BOHRIAN INTERPRETATION . . . 43 2.4 VAEXJOE
INTERPRETATION 44 2.5 INDIVIDUAL EMPIRICISTS INTERPRETATION - DIRAC-VON
NEUMANN INTER- PRETATION 45 2.6 INDIVIDUAL INTERPRETATION AND SUBJECTIVE
PROBABILITY - FUCHSIAN IN- TERPRETATION 45 2.7 PREPARATION AND
MEASUREMENT PROCEDURES 46 2.8 FILTERS - PREPARATION VIA SELECTION 47 2.9
PREPARATION AND MEASUREMENT PROCEDURES IN QUANTUM FORMALISM . 47 3
'CONTRADICTION' BETWEEN QUANTUM AND CLASSICAL PROBABILITY CALCULI . . .
48 3.1 ENSEMBLE APPROACH: DISTURBANCE EFFECTS 49 3.2 ENSEMBLE APPROACH:
NO CONDITIONAL PROBABILITIES 50 3.3 FREQUENCY PROBABILITY VIEWPOINT TO
QUANTUM PROBABILISTIC RULE . . 52 3.4 KOLMOGOROV FORMALISM AND QUANTUM
MEASUREMENTS 54 3.5 INTERFERENCE 55 3.6 NON-ERGODIC INTERPRETATION OF
QUANTUM MECHANICS 56 4 PROBABILITIES WITH RESPECT TO OBJECTIVE
CONDITIONS 57 4.1 FREQUENCY PROBABILITIES 58 4.2 NO CONDITIONAL
PROBABILITIES, NO BAYES' FORMULA 59 5 EINSTEIN-PODOLSKY-ROSEN PARADOX:
PROBABILITY, REALITY AND LOCALITY . . . 61 6 BELL'S INEQUALITY 65 6.
CONTENTS XIX 3 NEGATIVE PROBABILITIES 85 1 THE ORIGIN OF NEGATIVE
PROBABILITIES IN THE ENSEMBLE AND FREQUENCY THEORIES 85 1.1 ENSEMBLE
APPROACH: FLUCTUATIONSOF FINITEAPPROXIMATIONS 85 1.2 ENSEMBLE APPROACH:
SPLIT OF CONVENTIONAL PROBABILITIES 85 1.3 FREQUENCY APPROACH:
IRREGULARITY OF BEHAVIOUR OF FREQUENCIES . 86 1.4 FREQUENCY APPROACH:
SPLIT OF MISES' PROBABILITIES 87 1.5 WHERE ARE NEGATIVE PROBABILITIES?
87 1.6 THE FORMULA OF TOTAL PROBABILITY AS AN AVERAGE PROCEDURE 88 1.7
NEGATIVE PROBABILITIES AND THE PRINCIPLE OF COMPLEMENTARITY . . 90 1.8
HISTORY OF NEGATIVE PROBABILITIES IN PHYSICS 93 2 SIGNED 'PROBABILISTIC'
MEASURES AND EINSTEIN-PODOLSKY-ROSEN PARADOX 94 3 WIGNER PHASE-SPACE
DISTRIBUTION AND NEGATIVE PROBABILITY 101 4 DIRAC'S WORLD WITH NEGATIVE
PROBABILITIES 107 5 NEGATIVE PROBABILITIES AND LOCALIZATION 110 4 P-ADIC
PROBABILITY THEORY 113 1 NON-ARCHIMEDEAN NUMBER SYSTEMS; P-ADIC NUMBERS
115 2 FREQUENCY PROBABILITY THEORY 119 3 ENSEMBLE PROBABILITY '. 122 3.1
ENSEMBLES OF INFINITE VOLUMES 122 3.2 THE RULES FOR WORKING WITH P-ADIC
PROBABILITIES 126 3.3 NEGATIVE PROBABILITIES AND P-ADIC ENSEMBLE
PROBABILITIES 130 4 MEASURES 131 5 P-ADIC PROBABILITY SPACE 137 5 TESTS
FOR RANDOMNESS FOR P-ADIC PROBABILITY THEORY 140 1 P-ADI XX CONTENTS 2
5-SEQUENCES (COLLECTIVES) AND CORRESPONDING PROBABILITIES 166 3 FORMULA
OF TOTAL PROBABILITY AND MEASURES OF SUPPLEMENTARITY 167 4 SUPPLEMENTARY
PHYSICAL OBSERVABLES 171 5 PRINCIPLE OF SUPPLEMENTARITY 172 6
SUPPLEMENTARITY AND KOLMOGOROVNESS 173 7 QUANTUM-LIKE REPRESENTATION 178
1 TRIGONOMETRIE, HYPERBOLIC, AND HYPER-TRIGONOMETRIC CONTEXTS 178 2
QUANTUM-LIKE REPRESENTATION ALGORITHM - QLRA 180 2.1 PROBABILISTIC DATA
ABOUT CONTEXT 180 2.2 CONSTRUCTION OF COMPLEX PROBABILISTIC AMPLITUDES .
181 3 HUBERT SPACE REPRESENTATION OF FE-OBSERVABLE . 183 3.1 BORN'SRULE
. 183 3.2 FUNDAMENTAL PHYSICAL OBSERVABLE: VIEWS OF DE BROGLIE AND BOEHM
183 3.3 6-OBSERVABLE AS MULTIPLICATION OPERATOR 184 3.4 INTERFERENCE 185
4 HUBERT SPACE REPRESENTATION OFA -OBSERVABLE 185 4.1 CONVENTIONAL
QUANTUM AND QUANTUM-LIKE REPRESENTATIONS 185 4.2 A-BASIS FROM
INTERFERENCE 186 4.3 NECESSARY AND SUFFICIENT CONDITIONS FOR BORN'S RULE
187 4.4 CHOICE OF PROBABILISTIC PHASES 189 4.5 CONTEXTUAL DEPENDENCE OF
A-BASIS 189 4.6 EXISTENCE OF QUANTUM-LIKE REPRESENTATION WITH BORN'S
RULE FOR BOTH REFERENCE OBSERVABLES 190 4.7 "PATHOLOGIES" 191 5
PROPERTIES OF MAPPING OF TRIGONOMETRIC CONTEXTS INTO COMPLEX AMPLITUDES
192 5.1 CLASSICAL-LIKE CONTEXTS 192 5.2 NON-INJECTIVITY OF
REPRESENTATION MAP 193 6 NON-DOUBLY STOCHASTIC MATRIX: QUANTUM-LIKE
REPRESENTATIONS 193 7 |
| any_adam_object | 1 |
| author | Khrennikov, Andrei 1958- |
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| ctrlnum | (OCoLC)297144773 (DE-599)DNB991725050 |
| dewey-full | 519.2 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics 530 - Physics |
| dewey-raw | 519.2 530.12 |
| dewey-search | 519.2 530.12 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics 530 - Physics |
| discipline | Physik Mathematik |
| edition | 2., rev. and extended ed. |
| format | Book |
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| indexdate | 2024-07-20T10:08:34Z |
| institution | BVB |
| isbn | 9783110207484 |
| language | English |
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| spelling | Khrennikov, Andrei 1958- Verfasser (DE-588)128568410 aut Interpretations of probability Andrei Khrennikov 2., rev. and extended ed. Berlin [u.a.] de Gruyter 2009 XX, 217 S. 25 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 205 - 214 Wahrscheinlichkeitstheorie Quantentheorie Probabilities Quantum theory p-adic analysis Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3194509&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017374045&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Khrennikov, Andrei 1958- Interpretations of probability Wahrscheinlichkeitstheorie Quantentheorie Probabilities Quantum theory p-adic analysis Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4079013-7 |
| title | Interpretations of probability |
| title_auth | Interpretations of probability |
| title_exact_search | Interpretations of probability |
| title_full | Interpretations of probability Andrei Khrennikov |
| title_fullStr | Interpretations of probability Andrei Khrennikov |
| title_full_unstemmed | Interpretations of probability Andrei Khrennikov |
| title_short | Interpretations of probability |
| title_sort | interpretations of probability |
| topic | Wahrscheinlichkeitstheorie Quantentheorie Probabilities Quantum theory p-adic analysis Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Wahrscheinlichkeitstheorie Quantentheorie Probabilities Quantum theory p-adic analysis |
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