Translation invariance and finite additivity in a probability measure on the natural numbers.
Gardner, Robert, Price, Robert (2002)
International Journal of Mathematics and Mathematical Sciences
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Gardner, Robert, Price, Robert (2002)
International Journal of Mathematics and Mathematical Sciences
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Sergei V. Ovchinnikov, Jean Claude Falmagne (2003)
Mathware and Soft Computing
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We establish a necessary and sufficient condition for a function defined on a subset of an algebra of sets to be extendable to a positive additive function on the algebra. It is algo shown that this condition is necessary and sufficient for a regular function defined on a regular subset of the Borel algebra of subsets of a given compact Hausdorff space to be extendable to a measure.
Patrizia Berti, Luca Pratelli, Pietro Rigo, Fabio Spizzichino (2015)
Dependence Modeling
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Let (X,A) and (Y,B) be measurable spaces. Supposewe are given a probability α on A, a probability β on B and a probability μ on the product σ-field A ⊗ B. Is there a probability ν on A⊗B, with marginals α and β, such that ν ≪ μ or ν ~ μ ? Such a ν, provided it exists, may be useful with regard to equivalent martingale measures and mass transportation. Various conditions for the existence of ν are provided, distinguishing ν ≪ μ from ν ~ μ.
Zdena Riečanová (1972)
Časopis pro pěstování matematiky
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