Skip to main content
SpringerLink
Log in

Measures on product spaces and the existence of strong Baire liftings

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

Some notions are introduced for studying measures on product spaces, the main concept being that of property (*). In case when the topological factors are separable metric spaces, this property is equivalent to the completion regularity. We prove that (*) is preserved under arbitrary products of measure spaces. As a consequence, we deduce a series of related results in measure theory (some of which are known). In particular, the following extension of a result by Losert is obtained: Subject to CH, every product of ⩽ℵ2 many completion regular measures, each supported on any product of ⩽ℵ1 many compact metric spaces admits a strong Baire lifting.

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

References

  1. Choksi, J. R.: Recent developments arising out of Kakutani's work on completion regularity of measures. Contemp. Math.26, 81–94 (1984).

    Google Scholar 

  2. Choksi, J. R., Fremlin, D. H.: Completion regular measures on product spaces. Math. Ann.241, 113–128 (1979).

    Google Scholar 

  3. Fremlin, D. H.: Products of Radon measures: a counterexample. Canad. Math. Bull.19, 285–289 (1976).

    Google Scholar 

  4. Fremlin, D. H.: Note of 2/6/82.

  5. Grekas, S., Gryllakis, C.: Completion regular measures on product spaces with application to the existence of Baire strong liftings. Illinois J. Math.,35, 260–268 (1991).

    Google Scholar 

  6. Gryllakis, C.: Products of completion regular measures. Proc. Amer. Math. Soc.103, 563–568 (1988).

    Google Scholar 

  7. Gryllakis, C.: Homeomorphic, measures on products of intervals. Math. Ann.284, 377–389 (1989).

    Google Scholar 

  8. Gryllakis, C., Koumoullis, G.: Completion regularity and τ-additivity of measures on product spaces. Compos. Math.73, 329–344 (1990).

    Google Scholar 

  9. Jech, T.: Set Theory. New York: Academic Press. 1978.

    Google Scholar 

  10. Kakutani, S.: Notes on infinite product measures II. Proc. Imperial Acad. Tokyo19, 184–188 (1943).

    Google Scholar 

  11. Losert, V.: A counterexample on measurable selections and strong lifting. In: Measure Theory Oberwolfach 1979 (Ed.:D. Kölzow). Lect. Notes Math.794, 153–159. Berlin-Heidelberg-New York: Springer. 1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Zografou, Box 64075, 15710, Athens, Greece

    S. Grekas & C. Gryllakis

Authors
  1. S. Grekas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Gryllakis
    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

Grekas, S., Gryllakis, C. Measures on product spaces and the existence of strong Baire liftings. Monatshefte für Mathematik 114, 63–76 (1992). https://doi.org/10.1007/BF01572080

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01572080

Keywords

Search

Navigation