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Borel extensions of Baire measures

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We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space is Mařík, that under "c is real-valued measurable", a Baire subset of a Mařík space need not be Mařík, and finally, that the preimage of a Mařík space under an open perfect map is Mařík.
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  • Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain,
  • [Ad1] W. Adamski, On regular extensions of contents and measures, J. Math. Anal. Appl. 127 (1987), 211-225.
  • [Ad2] W. Adamski, On the interplay between a topology and its associated Baire and Borel σ-algebra, Period. Math. Hungar. 21 (2) (1987), 85-93.
  • [Ad3] W. Adamski, τ-smooth Borel measures on topological spaces, Math. Nachr. 78 (1977), 97-107.
  • [Ba] W. Bade, Two properties of the Sorgenfrey plane, Pacific J. Math. 51 (1974), 349-354.
  • [Be] M. G. Bell, On the combinatorial principle P(c), Fund. Math. 114 (1981), 149-157.
  • [BB] K. P. S. Bhaskara Rao and M. Bhaskara Rao, Theory of Charges, Academic Press, 1983.
  • [vD] E. K. van Douwen, Covering and separation properties of box products, in: Surveys in General Topology, G. M. Reed (ed.), Academic Press, 1980, 55-129.
  • [Do] C. H. Dowker, On countably paracompact spaces, Canad. J. Math. 3 (1951), 219-224.
  • [Eng] R. Engelking, General Topology, Heldermann, Berlin, 1989.
  • [F1] D. H. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, 1984.
  • [F2] D. H. Fremlin, Real-valued-measurable cardinals, in: Set Theory of the Reals, H. Judah (ed.), Israel Math. Conf. Proc. 6, Bar-Ilan Univ., Ramat Gan, 1993, 151-304.
  • [F3] D. H. Fremlin, Uncountable powers of ℝ can be almost Lindelöf, Manuscripta Math. 22 (1977), 77-85.
  • [Fro] Z. Frolík, Applications of complete families of continuous functions to the theory of Q-spaces, Czechoslovak Math. J. 11 (1961), 115-133.
  • [GJ] L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nostrand, Princeton, N.J., 1989.
  • [Grz] E. Grzegorek, Solution of a problem of Banach on σ-fields without continuous measures, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), 7-10.
  • [HRR] A. W. Hager, G. D. Reynolds and M. D. Rice, Borel-complete topological spaces, Fund. Math. 75 (1972), 135-143.
  • [Ish] F. Ishikawa, On countably paracompact spaces, Proc. Japan Acad. 31 (1955), 686-687.
  • [Ka] A. Kato, Union of realcompact spaces and Lindelöf spaces, Canad. J. Math. 31 (1979), 1247-1268.
  • [Ki] R. B. Kirk, Locally compact, B-compact spaces, Indag. Math. 31 (1969), 333-344.
  • [Kn] J. D. Knowles, Measures on topological spaces, Proc. London Math. Soc. (3) 17 (1967), 139-156.
  • [Ku] K. Kunen, Inaccessibility properties of cardinals, Ph.D. thesis, Stanford Univ., 1968.
  • [Lem] J. Lembcke, Konservative Abbildungen und Fortsetzung regulärer Masse, Z. Wahrsch. Verw. Gebiete 15 (1970), 57-96.
  • [Ma] J. Mařík, The Baire and Borel measure, Czechoslovak Math. J. 7 (1957), 248-253.
  • [Mo] W. Moran, The additivity of measures on completely regular spaces, J. London Math. Soc. 43 (1968), 633-639.
  • [Na] K. Nagami, Countable paracompactness of inverse limits and products, Fund. Math. 73 (1972), 261-270.
  • [OT] H. Ohta and K. Tamano, Topological spaces whose Baire measure admits a regular Borel extension, Trans. Amer. Math. Soc. 317 (1990), 393-415.
  • [Ost] A. J. Ostaszewski, On countably compact, perfectly normal spaces, J. London Math. Soc. (2) 14 (1976), 505-516.
  • [Ox] J. C. Oxtoby, Homeomorphic measures in metric spaces, Proc. Amer. Math. Soc. 24 (1970), 419-423.
  • [Pa] J. K. Pachl, Disintegration and compact measures, Math. Scand. 43 (1978), 157-168.
  • [Ru1] M. E. Rudin, Dowker spaces, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), North-Holland, 1984, 761-780.
  • [Ru2] M. E. Rudin, A normal space X for which X × I is not normal, Fund. Math. 73 (1971), 179-186.
  • [S] B. M. Scott, Some "almost-Dowker" spaces, Proc. Amer. Math. Soc. 68 (1978), 359-364.
  • [SS] L. A. Steen and J. A. Seebach, Counterexamples in Topology, Springer, 1986.
  • [St] A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. 58 (1948), 977-982.
  • [Sz] P. J. Szeptycki, Dowker spaces, in: Topology Atlas 1, D. Shakhmatov and S. Watson (eds.), electronic publication, 1996, 45-47.
  • [T] F. Topsœ, On construction of measures, in: Proc. Conf. "Topology and Measure I" (Zinnowitz 1974), Part 2, J. Flachsmeyer, Z. Frolík and F. Terpe (eds.), Ernst-Moritz-Arndt Univ., Greifswald, 1978, 343-381.
  • [U] S. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math. 16 (1930), 140-150.
  • [W] W. Weiss, Versions of Martin's axiom, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), North-Holland, 1984, 827-886.
  • [Wh1] R. F. Wheeler, A survey of Baire measures and strict topologies, Exposition. Math. 77 (1983), 97-190.
  • [Wh2] R. F. Wheeler, Extensions of a σ-additive measure to the projective cover, in: Lecture Notes in Math. 794, Springer, 1980, 81-104.
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