Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
An example of an irregular random measure
Download PDF
Download PDF
  • Published: June 1990

An example of an irregular random measure

  • Sylvie Guerre-Delabriere1 

Probability Theory and Related Fields volume 86, pages 155–165 (1990)Cite this article

  • 64 Accesses

  • Metrics details

Summary

We consider the set of random measures which consists of measurable mapsω→μ ω from [0, 1] to the set of measures on ℝ. As it is the dual space ofL 1 ([0, 1];C(

)), we can equip this space with the weak* topology. We construct a special random measure μ, which appears as the weak* limit of a sequence of Dirac random measures\(\left( {\delta _{X_n } } \right)_{n \in \mathbb{N}}\), where (X n ) n∈ℕ is a bounded sequence inL p [0, 1], (1≦p<2). The special form of this random measure, which oscillates randomly between twoq-stable standard measures on ℝ with different normalizations (p<q<2) allows us to prove two properties of (X n ) n∈ℕ is equivalent to the unit vector basis ofl q and has no almost symmetric subsequence.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  • [A] Aldous, D.J.: Subspaces ofL 1 via random measures. Trans. Am. Math. Soc.267, 445–463 (1981)

    Google Scholar 

  • [BR] Berkes, I., Rosenthal, H.P.: Almost exchangeable sequences of random variables. Z. Warscheinlichkeitstheor.70, 473–507 (1985)

    Google Scholar 

  • [D] Doeblin, W.: Ensembles de puissances d'une loi de probabilité. Stud. Math.9, 71–96 (1940)

    Google Scholar 

  • [F] Feller, W.: An introduction to probability theory and its applications, vols.I, II. New York: Wiley 1966

    Google Scholar 

  • [G1] Guerre, S.: Types et suites symétriques dansL p , 1≦p<+∞,p≠2. Isr. J. Math.53, 191–208 (1986)

    Google Scholar 

  • [G2] Guerre, S.: Sur les suites presques échangeables dansL q , 1≦q<2. Isr. J. Math.56, 361–380 (1986)

    Google Scholar 

  • [GR] Guerre, S., Raynaud, Y.: On sequences with no almost symmetric subsequence. Loghorn Notes-UT Funct. Anal. Seminar (Austin-Texas, 1985–86)

  • [L] Levy, P.: Théorie de l'addition des variables aléatoires. Paris: Gauthier-Villars (1937)

    Google Scholar 

  • [LT] Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces, vols. I, II. Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  • [M] Maurey, B.: Tout sous-espaces deL 1 contient unl p d'après D. Aldous. Séminaire d'Analyse Fonctionnelle. Ecole Polytechnique (1979–80)

  • [R] Raynaud, Y.: Extracting almost symmetric sequences in r.i. spaces. Math. Proc. Camb. Philos. Soc.104, 303–316 (1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Equipe d'analyse, Université Paris-6, Tour 46, 4ème étage, 4 Place Jussieu, F-75252, Paris Cedex 05, France

    Sylvie Guerre-Delabriere

Authors
  1. Sylvie Guerre-Delabriere
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Guerre-Delabriere, S. An example of an irregular random measure. Probab. Th. Rel. Fields 86, 155–165 (1990). https://doi.org/10.1007/BF01474640

Download citation

  • Received: 15 February 1989

  • Revised: 24 November 1989

  • Issue Date: June 1990

  • DOI: https://doi.org/10.1007/BF01474640

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Stochastic Process
  • Unit Vector
  • Probability Theory
  • Special Form
  • Vector Basis
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature