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Foundations of non-commutative probability theory [PDF]

open access: possibleProceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge, 2009
Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables, are defined in a natural way.
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Foundations of a quantum probability theory

Journal of Mathematical Physics, 1975
Statistical physical theories are frequently formulated in terms of probabilistic structures founded on a ’’logic of experimentally verifiable propositions.’’ It is argued that to each experimentally verifiable proposition there corresponds an experimental procedure which, in general, alters the state of the system, and is completely characterized by a
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On the Foundations of the Theory of Probabilities

Philosophy of Science, 1934
The foundation of the mathematical theory of probabilities is still a controversial subject. There are schools of insufficient reasoning and of cogent reasoning, of a priori determination and of frequency determination, of subjective and of objective probability. Two main difficulties exist. The first is the definition of equally like events.
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Foundations of the Theory of Probability and the Theory of Errors

1973
Random event. If a certain event, in given circumstances, may occur or may not occur, then it is called a random event. The probability of a random event is a quantitative estimation of the probability of its occurrence.
I. N. Bronshtein, K. A. Semendyayev
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Foundations of Probability Theory

2009
This chapter contains sections titled: Historical Background Approaches to the Definition of Probability The Concept of Probability The Field of Events Classical Definition of Probability Random Variables Numerical Characteristics of Random Variables Basic Rules of Operation Computing Conditional ...
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