A remark on a paper of B. R. Gelbaum

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete volume 43, pages353–355(1978)Cite this article

Summary

In this paper the following generalization of a theorem by B.R. Gelbaum is proved:

Let (K, d) be a compact, connected metric space. Let B denote the Borel sets of (K, d), and P be a probability measure on B with P(G)≠O for any nonempty open G, f, gεC(K,d) independent random variables on (K,B,P) and let g satisfy the following assumption:

There is an y o∃ℝ such that g −1(y0) is a finite nonempty set. Then f is a constant function.

Examples show that the assumptions of this theorem are essential.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

US$ 39.95

Tax calculation will be finalised during checkout.

Reference

  1. 1.

    Gelbaum, B.R.: Independence of events and of random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 36, 333–343 (1976)

    Google Scholar 

Download references

Author information

Affiliations

  1. Department of Probability Theory, University L. Eötvös, Muzeum körut 6–8, H-1088, Budapest, Hungary

    A. P. Bosznay

Authors
  1. A. P. Bosznay
    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

Bosznay, A.P. A remark on a paper of B. R. Gelbaum. Z. Wahrscheinlichkeitstheorie verw Gebiete 43, 353–355 (1978). https://doi.org/10.1007/BF00534768

Download citation

Keywords

  • Stochastic Process
  • Probability Measure
  • Probability Theory
  • Mathematical Biology
  • Constant Function