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Foundations of non-commutative probability theory [PDF]

open access: greenProceedings 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.
Daniel Lehmann
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Mathematical Foundations of Probability Theory

open access: closed, 1984
The theory of probability, as a mathematical discipline, can and should be developed from axioms in exactly the same way as Geometry and Algebra. This means that after we have defined the elements to be studied and their basic relations, and have stated the axioms by which these relations are to be governed, all further exposition must be based ...
A. N. Shiryaev
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