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1995 | 147 | 1 | 27-37
Tytuł artykułu

Products of completion regular measures

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
147
Numer
1
Strony
27-37
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-02-15
Twórcy
  • Mathematics Department, University of Essex, Colchester CO4 3SQ, England, fremdh@essex.ac.uk
autor
  • Section of Mathematical Analysis, Panepistemiopolis, 15784 Athens, Greece
Bibliografia
  • [1] J. Choksi and D. H. Fremlin, Completion regular measures on product spaces, Math. Ann. 241 (1979), 113-128.
  • [2] W. W. Comfort, K.-H. Hoffmann and D. Remus, Topological groups and semigroups, pp. 57-114 in [11].
  • [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.
  • [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.
  • [8] C. Gryllakis, Products of completion regular measures, Proc. Amer. Math. Soc. 103 (1988), 563-568.
  • [9] C. Gryllakis and G. Koumoullis, Completion regularity and τ-additivity of measures on product spaces, Compositio Math. 73 (1990), 329-344.
  • [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.
  • [13] S. Kakutani and K. Kodaira, Über das Haarsche Mass in der lokal bikompakten Gruppe, ibid. 20 (1944), 444-450.
  • [14] K. Kunen, Set Theory, North-Holland, 1980.
  • [15] K. Kunen and J. E. Vaughan (eds.), Handbook of Set-Theoretic Topology, North-Holland, 1984.
  • [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.
  • [18] P. Ressel, Some continuity and measurability results on spaces of measures, Math. Scand. 40 (1977), 69-78.
  • [19] K. A. Ross and A. H. Stone, Products of separable spaces, Amer. Math. Monthly 71 (1964), 398-403.
  • [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].
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv147i1p27bwm
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