Skip to main content
SpringerLink
Log in
Book cover

Selected Works of R.M. Dudley pp 28–37Cite as

Distances of Probability Measures and Random Variables

  • Chapter
  • First Online:

Part of the book series: Selected Works in Probability and Statistics ((SWPS))

Abstract

Let (S, d) be a separable metric space. Let \( P; > \left( S \right)\) be the set of Borel probability measures on S. \(C\left( S \right)\) denotes the Banach space of bounded continuous real-valued functions on S, with norm

$$\left\| f \right\|_\infty= \sup \left\{ {\left| {f\left( x \right)} \right|:x{\text{ }}\varepsilon {\text{ }}S} \right\}.$$

Received 11 January 1968.

Fellow of the A. P. Sloan Foundation.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dudley, R. M. (1966). Convergence of Baire measures. Studia Math. 27 251–268.

    MATH  MathSciNet  Google Scholar 

  2. Fortet, Robert (1958). Recent advances in probability theory. Some Aspects of Analysis and Probability. Wiley, New York.

    Google Scholar 

  3. Fortet, Robert and E. Mourier (1953). Convergence de la répartition empirique vers la répartition théorique. Ann. Sci. Ecole Norm. Sup. 70 266–285.

    MathSciNet  Google Scholar 

  4. Gnedenko, B. V., and A. N. Kolmogorov (1954). Limit Distributions for Sums of Independent Random Variables (transl. by K. L. Chung). Addison-Wesley, Reading, Mass.

    Google Scholar 

  5. Hall, M. (1958). A survey of combinatorial analysis. Some Aspects of Analysis and Probability. Wiley, New York.

    Google Scholar 

  6. Hall, P. (1935). On representatives of subsets. J. London Math. Soc. 10 26–30.

    Article  MATH  Google Scholar 

  7. Halmos, P. (1950). Measure Theory. Van Nostrand, Princeton.

    MATH  Google Scholar 

  8. Kolmogorov, M. N. (1963). Approximation to distributions of sums of independent terms by means of infinitely divisible distributions. Trans. Moscow Math. Soc. 12 492–509.

    MATH  MathSciNet  Google Scholar 

  9. Prokhorov, Yu. V. (1956). Convergence of random processes and limit theorems in probability theory. Theor. Prob. Appl. 1 157–214.

    Article  Google Scholar 

  10. Skorokhod, A. V. (1956). Limit theorems for stochastic processes. Theor. Prob. Appl. 1 261–290.

    Article  Google Scholar 

  11. Strassen, V. (1965). The existence of probability measures with given marginals. Ann. Math. Statist. 36 423–439.

    Article  MATH  MathSciNet  Google Scholar 

  12. Varadarajan, V. S. (1961). Measures on topological spaces. Amer. Math. Soc. Transl. Series 2, 48 161–228.

    Google Scholar 

  13. Zygmund, Antoni (1959). Trigonometrical Series. Cambridge Univ. Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    R. M. Dudley

Authors
  1. R. M. Dudley
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. , Mathematics, University of Connecticut, Auditorium Road 196, Storrs, 06269-3009, USA

    Evarist Giné

  2. , Mathematics, Georgia Institute of Technology, Atlanta, 30332-0160, USA

    Vladimir Koltchinskii

  3. Inst. Mathematics & Informatics, Akademijos 4, Vilnius, LT-08663, Lithuania

    Rimas Norvaisa

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Dudley, R.M. (2010). Distances of Probability Measures and Random Variables. In: Giné, E., Koltchinskii, V., Norvaisa, R. (eds) Selected Works of R.M. Dudley. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5821-1_4

Download citation

Publish with us

Policies and ethics

Search

Navigation