Approximating Radon measures on first-countable compact spaces

• Autorzy: Grzegorz Plebanek
• Języki publikacji: EN

Abstrakty

EN

The assertion every Radon measure defined on a first-countable compact space is uniformly regular is shown to be relatively consistent. We prove an analogous result on the existence of uniformly distributed sequences in compact spaces of small character. We also present two related examples constructed under CH.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 86
• Numer: 1
• Strony: 15-23

Daty

wydano

2000

otrzymano

1999-03-29

Twórcy

autor

Grzegorz Plebanek

• Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] A. G. Babiker, On uniformly regular topological measure spaces, Duke Math. J. 43 (1976), 775-789.
• [2] M. Džamonja and K. Kunen, Measures on compact HS spaces, Fund. Math. 143 (1993), 41-54.
• [3] R. Frankiewicz and G. Plebanek, On asymptotic density and uniformly distributed sequences, Studia Math. 119 (1996),17-26.
• [4] R. Frankiewicz, G. Plebanek and C. Ryll-Nardzewski, Between Lindelöf property and countable tightness, Proc. Amer. Math. Soc., to appear.
• [5] D. H. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, Cambridge, 1984.
• [6] D. H. Fremlin, Measure algebras, in: Handbook of Boolean Algebras, J. D. Monk (ed.), North-Holland, 1989, Vol. III, Chap. 22.
• [7] D. H. Fremlin, Real-valued-measurable cardinals, in: Set Theory of the Reals, H. Judah (ed.), Israel Math. Conf. Proc. 6, Bar-Ilan Univ., 1993, 151-304.
• [8] D. H. Fremlin, On compact spaces carrying Radon measures of uncountable Maharam type, Fund. Math. 154 (1997), 295-304.
• [9] D. H. Fremlin, Problems, September 1998.
• [10] R. Haydon, On dual $L^1$-spaces and injective bidual Banach spaces, Israel J. Math. 31 (1978), 142-152.
• [11] J. Kraszewski, Properties of ideals on the generalized Cantor spaces, doctoral dissertation, Wrocław, 1999 (available from [e-mail]).
• [12] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974.
• [13] K. Kunen, A compact L-space under CH, Topology Appl. 12 (1981), 283-287.
• [14] K. Kunen and J. van Mill, Measures on Corson compact spaces, Fund. Math. 147 (1995), 61-72.
• [15] V. Losert, On the existence of uniformly distributed sequences in compact topological spaces II, Monatsh. Math. 87 (1979), 247-260.
• [16] S. Mercourakis, Some remarks on countably determined measures and uniform distribution of sequences, ibid. 121 (1996), 79-101.
• [17] D. Plachky, Extremal and monogenic additive set functions, Proc. Amer. Math. Soc. 54 (1976), 193-196.
• [18] G. Plebanek, On Radon measures on first-countable spaces, Fund. Math. 148 (1995), 159-164.
• [19] G. Plebanek, Nonseparable Radon measures and small compact spaces, ibid. 153 (1997), 25-40.
• [20] R. Pol, Note on the spaces of regular probability measures whose topology is determined by countable subsets, Pacific J. Math. 100 (1982), 185-201.
• [21] J. E. Vaughan, Small uncountable cardinals and topology, in: Open Problems in Topology, J. van Mill and G. M. Reed (eds.), North-Holland, 1990, Chap. 11.