Skip to main content
SpringerLink
Log in

The existence of probability measures with specified projections

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

Let X and Y be locally compactσ-compact topological spaces, F ⊂X×Y is closed, and P(F) is the set of all Borel probability measures on F. For us to find, for the pair of probability measures (μx, μy εP (X)×P(Y), a probability measureμ ε P(F) such that μ X =μΠ −1 X , μ Y =μΠ −1 Y it is necessary and sufficient that, for any pair of Borel sets A ⊂X, B ⊂Y for which (A× B) ∩ F=Ø, the conditionμ XA+μ YB ≤ 1 holds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. V. Strassen, “Probability measures with given marginals,” American Mathematical Society,36, No. 2 (1965).

  2. V. N. Sudakov, “On the existence of bistochastic planes,” Zipiski Nauchnykh Seminarov LOMI,29, Leningrad (1972).

Download references

Author information

Authors and Affiliations

  1. Leningrad Branch, V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR, USSR

    V. N. Sudakov

Authors
  1. V. N. Sudakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 573–576, October, 1973.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sudakov, V.N. The existence of probability measures with specified projections. Mathematical Notes of the Academy of Sciences of the USSR 14, 886–888 (1973). https://doi.org/10.1007/BF01108820

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01108820

Keywords

Search

Navigation