# Products of completion regular measures

Fundamenta Mathematicae (1995)

- Volume: 147, Issue: 1, page 27-37
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topFremlin, David, and Grekas, S.. "Products of completion regular measures." Fundamenta Mathematicae 147.1 (1995): 27-37. <http://eudml.org/doc/212072>.

@article{Fremlin1995,

abstract = {We investigate the products of topological measure spaces, discussing conditions under which all open sets will be measurable for the simple completed product measure, and under which the product of completion regular measures will be completion regular. In passing, we describe a new class of spaces on which all completion regular Borel probability measures are τ-additive, and which have other interesting properties.},

author = {Fremlin, David, Grekas, S.},

journal = {Fundamenta Mathematicae},

keywords = {-additive measure; dyadic Hausdorff space; products; topological measure spaces; completion regular measures},

language = {eng},

number = {1},

pages = {27-37},

title = {Products of completion regular measures},

url = {http://eudml.org/doc/212072},

volume = {147},

year = {1995},

}

TY - JOUR

AU - Fremlin, David

AU - Grekas, S.

TI - Products of completion regular measures

JO - Fundamenta Mathematicae

PY - 1995

VL - 147

IS - 1

SP - 27

EP - 37

AB - We investigate the products of topological measure spaces, discussing conditions under which all open sets will be measurable for the simple completed product measure, and under which the product of completion regular measures will be completion regular. In passing, we describe a new class of spaces on which all completion regular Borel probability measures are τ-additive, and which have other interesting properties.

LA - eng

KW - -additive measure; dyadic Hausdorff space; products; topological measure spaces; completion regular measures

UR - http://eudml.org/doc/212072

ER -

## References

top- [1] J. Choksi and D. H. Fremlin, Completion regular measures on product spaces, Math. Ann. 241 (1979), 113-128. Zbl0387.60006
- [2] W. W. Comfort, K.-H. Hoffmann and D. Remus, Topological groups and semigroups, pp. 57-114 in [11]. Zbl0798.22001
- [3] R. Engelking, General Topology, Sigma Ser. Pure Math. 6, Heldermann, 1989.
- [4] D. H. Fremlin, Products of Radon measures: a counterexample, Canad. Math. Bull. 19 (1976), 285-289. Zbl0353.28005
- [5] Z. Frolík (ed.), General Topology and its Relations to Modern Analysis and Algebra VI, Proc. Sixth Prague Topological Sympos., 1986, Heldermann, 1988.
- [6] R. J. Gardner and W. F. Pfeffer, Borel measures, pp. 961-1043 in [15].
- [7] S. Grekas and C. Gryllakis, Completion regular measures on product spaces with application to the existence of Baire strong liftings, Illinois J. Math. 35 (1991), 260-268. Zbl0714.28009
- [8] C. Gryllakis, Products of completion regular measures, Proc. Amer. Math. Soc. 103 (1988), 563-568. Zbl0655.28005
- [9] C. Gryllakis and G. Koumoullis, Completion regularity and τ-additivity of measures on product spaces, Compositio Math. 73 (1990), 329-344. Zbl0719.28005
- [10] P. Halmos, Measure Theory, van Nostrand, 1950.
- [11] M. Hušek and J. van Mill (eds.), Recent Progress in General Topology, Elsevier, 1992.
- [12] S. Kakutani, Notes on infinite product spaces II, Proc. Imperial Acad. Tokyo 19 (1943), 184-188. Zbl0061.09701
- [13] S. Kakutani and K. Kodaira, Über das Haarsche Mass in der lokal bikompakten Gruppe, ibid. 20 (1944), 444-450. Zbl0060.13501
- [14] K. Kunen, Set Theory, North-Holland, 1980.
- [15] K. Kunen and J. E. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, 1984. Zbl0546.00022
- [16] V. Kuz'minov, On a hypothesis of P. S. Aleksandrov in the theory of topological groups, Dokl. Akad. Nauk SSSR 125 (1959), 727-729 (in Russian).
- [17] W. Moran, The additivity of measures on completely regular spaces, J. London Math. Soc. 43 (1968), 633-639. Zbl0159.07802
- [18] P. Ressel, Some continuity and measurability results on spaces of measures, Math. Scand. 40 (1977), 69-78. Zbl0372.28010
- [19] K. A. Ross and A. H. Stone, Products of separable spaces, Amer. Math. Monthly 71 (1964), 398-403. Zbl0119.38202
- [20] M. Talagrand, Pettis integral and measure theory, Mem. Amer. Math. Soc. 307 (1984).
- [21] V. V. Uspenskiĭ, Why compact groups are dyadic, pp. 601-610 in [5].

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.