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Interpretations of Probability

Contents:

Introduction
I. FOUNDATIONS OF PROBABILITY THEORY
A few words about measures
Classical and ensemble definitions of probability
Frequency theory of probability
Kolmogorov=s measure-theoretical approach
Kolmogorov=s ideas on probability
Measure-theoretical approach and interpretations of probability
Subjective (Bayesian) probability theory
Foundations of randomness
Operation of combining of collectives
Independence of collectives
Frequency and measure-theoretical viewpoints on independence
Generalization of the operation of combining
Comparative probability
II. QUANTUM PROBABILITIES
Classical and quantum probability rules
Physical interpretations of the wave function
`Contradiction' between quantum and classical probabilitycalculi
Probabilities with respect to objective conditions
Einstein-Poldolsky-Rosen paradox: Probability, reality, locality
Bell's inequality for probabilities
Bell's mystification
Bell's inequality for covariations
Hidden variables and Bell's inequality
III. NEGATIVE PROBABILITIES
The origin of negative probabilities in the ensemble and frequencytheories
Signed `probabilistic' measures and Einstein-Podolsky-Rosenparadox
Wiegener phase-space distribution and negative probability
Dirac's world with negative probabilities
Negative probabilities and localization
IV. P-ADIC PROBABILITY THEORY
Non-Archimedean number-systems; p-adic numbers
Frequency probability theory
Ensemble probability
Measures
p-Adic probability space
V. INFORMATION AND PROBABILITY
Information reality
Dynamics on information spaces
Information velocity, acceleration, mass and force, Newton's laws
Mathematical `pathologies'
Quantum mechanics on information spaces
The pilot wave theory for cognitive systems
Subjective probability as probability with respect to the statisticalensemble of human ideas
Bayes' theorem and Freud's psychoanalysis
VI. TESTS FOR RANDOMNESS FOR P-ADIC PROBABILITY THEORY
p-Adic probability measures on the space of binary sequences
Some technical p-adic results
p-Adic tests for randomness
Limit theorems
Recursive enumeration of the set of p-adic tests
No p-adic universal test
Randomness of infinite sequences
Bibliography
Index

1999; iv+228 pages
ISBN 90-6764-310-6
Price (all prices are subject to change without notice): EUR 152/US$ 217

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