Abstract
In classical probability theory one assumes that all the events concerning a statistical experiment constitute a Boolean σ-algebra and defines a probability measure as a completely additive non-negative function which assigns the value unity for the identity element of the σ-algebra. Invariably, the σ-algebra is the Borel σ-algebra \( \mathcal{B} \) X (i.e., the smallest σ-algebra generated by the open subsets) of a nice topological space X. Under very general conditions it turns out that all probability measures on \( \mathcal{B} \) X constitute a convex set whose extreme points are degenerate probability measures.
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© 2005 Hindustan Book Agency
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Parthasarathy, K.R. (2005). Probability Theory on the Lattice of Projections in a Hilbert Space. In: Mathematical Foundation of Quantum Mechanics. Texts and Readings in Mathematics, vol 35. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-28-6_1
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DOI: https://doi.org/10.1007/978-93-86279-28-6_1
Publisher Name: Hindustan Book Agency, Gurgaon
Print ISBN: 978-81-85931-59-3
Online ISBN: 978-93-86279-28-6
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