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Measures on two-dimensional products

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

Grzegorz Plebanek
Grzegorz Plebanek
Affiliation:
Institute of Mathematics, Wroclaw University, pl. Grunwaldzki 2/4, Wroclaw, Poland.
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Extract

§1. Introduction. Let two probability spaces (X, , μ,) and (Y, ℬ, ν) be given. For a subset D of X × Y and a real number d ≥ 0 we consider the following problem

(MP) Does there exist a measure » on X × Y having μ and ν as marginals and such that λ (D) ≥ 1 − d?

This problem comes from Strassen's paper [12], where Borel probabilities on Polish spaces were treated. Further, it was investigated by many authors in more general settings (cf. [2], [4]-[7], [11]-[13]).

MSC classification

Secondary: 28A35: Measures and integrals in product spaces
Type
Research Article
Information
Mathematika , Volume 36 , Issue 2 , December 1989 , pp. 253 - 258
Copyright
Copyright © University College London 1989

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References

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