Electronic Communications in Probability

Standard representation of multivariate functions on a general probability space

Svante Janson

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Abstract

It is well-known that a random variable, i.e. a function defined on a probability space, with values in a Borel space, can be represented on the special probability space consisting of the unit interval with Lebesgue measure. We show an extension of this to multivariate functions. This is motivated by some recent constructions of random graphs.

Article information

Source
Electron. Commun. Probab., Volume 14 (2009), paper no. 34, 343-346.

Dates
Accepted: 26 August 2009
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465234743

Digital Object Identifier
doi:10.1214/ECP.v14-1477

Mathematical Reviews number (MathSciNet)
MR2535082

Zentralblatt MATH identifier
1189.60011

Subjects
Primary: 60A10: Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx}

Keywords
Borel space random graphs

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Janson, Svante. Standard representation of multivariate functions on a general probability space. Electron. Commun. Probab. 14 (2009), paper no. 34, 343--346. doi:10.1214/ECP.v14-1477. https://projecteuclid.org/euclid.ecp/1465234743


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References

  • D. Aldous. Representations for partially exchangeable arrays of random variables. J. Multivar. Anal. 11 (1981), 581–598.
  • B. Bollobás, S. Janson and O. Riordan. The phase transition in inhomogeneous random graphs. Random Structures Algorithms 31 (2007), 3–122.
  • B. Bollobás, S. Janson and O. Riordan. Sparse random graphs with clustering. Preprint, 2008.
  • C. Borgs, J. T. Chayes, L. Lovász, V. T. Sós and K. Vesztergombi. Convergent sequences of dense graphs I: Subgraph frequencies, metric properties and testing. Preprint, 2007.
  • C. Borgs, J. T. Chayes, L. Lovász, V. T. Sós and K. Vesztergombi. Convergent sequences of dense graphs II: Multiway cuts and statistical physics. Preprint, 2007.
  • C. Dellacherie and P.-A. Meyer. Probabilités et potentiel. Édition entièrement refondue, Hermann, Paris, 1975
  • P. Diaconis and S. Janson. Graph limits and exchangeable random graphs. Rendiconti di Matematica 28 (2008), 33–61.
  • D. Hoover. Relations on Probability Spaces and Arrays of Random Variables. Preprint, Institute for Advanced Study, Princeton, NJ, 1979.
  • O. Kallenberg. Foundations of Modern Probability. 2nd ed., Springer, New York, 2002.
  • O. Kallenberg. Probabilistic Symmetries and Invariance Principles. Springer, New York, 2005.
  • L. Lovász and B. Szegedy. Limits of dense graph sequences. J. Comb. Theory B 96 (2006), 933–957.