Title:
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Small systems -- on approximation of compact sets of measurable functions to compact subsets of $C_{c-o}(X)$ (English) |
Author:
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Wajch, Eliza |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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41 |
Issue:
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4 |
Year:
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1991 |
Pages:
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619-633 |
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Category:
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math |
. |
MSC:
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28A20 |
MSC:
|
54C50 |
idZBL:
|
Zbl 0760.28003 |
idMR:
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MR1134952 |
DOI:
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10.21136/CMJ.1991.102494 |
. |
Date available:
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2008-06-09T15:42:00Z |
Last updated:
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2020-07-28 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/102494 |
. |
Reference:
|
[1] D. K. Burke: Covering properties.in: Handbook of Set-Theoretic Topology (K. Kunen, J. E. Vaughan, eds.), North Holland-Amsterdam, 1984, 347-422. Zbl 0569.54022, MR 0776628 |
Reference:
|
[2] F. Cafiero: Misura e lntegrazione.Rome, 1959, 308-315. |
Reference:
|
[3] P. Capek: On small systems.Acta Fac. Rerum Natur. Univ. Comenian Math. 34 (1979), 93-101. Zbl 0436.28003, MR 0568339 |
Reference:
|
[4] G. Choquet: Forme abstraite du théorème de capacitabilité.Ann. Inst. Fourier 9 (1959), 83-89. Zbl 0093.29701, MR 0112844, 10.5802/aif.87 |
Reference:
|
[5] R. Engelking: General Topology.Warsaw, 1977. Zbl 0373.54002, MR 0500780 |
Reference:
|
[6] M. Fréchet: Sur les ensembles compacts de fonctions measurables.Fund. Math. 9 (1927), 25-32. 10.4064/fm-9-1-25-32 |
Reference:
|
[7] R. J. Gardner, W. F. Pfeffer: Borel measures.in: Handbook of Set-Theoretic Topology (K. Kunen, J. E. Vaughan, eds.), North Holland-Amsterdam, 1984, 961-1043. Zbl 0593.28016, MR 0776641 |
Reference:
|
[8] L. Gillman, M.Jerison: Rings of Continuous Functions.New York-Heidelberg-Berlin, 1976. Zbl 0339.46018, MR 0407579 |
Reference:
|
[9] E. H. Hanson: A note on compactness.Bull. Amer. Math. Soc. 39 (1933), 397-400. Zbl 0007.15303, MR 1562635, 10.1090/S0002-9904-1933-05642-2 |
Reference:
|
[10] J. Hejduk, E. Wajch: Compactness in the sense of the convergence with respect to a small system.Math. Slov. 39 (1989), 267-275. Zbl 0681.28002, MR 1016344 |
Reference:
|
[11] A. Horn, A. Tarski: Measures in Boolean algebras.Trans. Amer. Math. Soc. 64 (1948), 467-497. MR 0028922, 10.1090/S0002-9947-1948-0028922-8 |
Reference:
|
[12] T. Jech: Set Theory.New York, 1978. Zbl 0419.03028, MR 0506523 |
Reference:
|
[13] R. A. Johnson J. Niewiarowski, T. Šwiątkowski: Small systems convergence and metrizability.Proc. Amer. Math. Soc. 103 (1988), 105-112. MR 0938652, 10.1090/S0002-9939-1988-0938652-4 |
Reference:
|
[14] J. L. Kelley: Measures on Boolean algebras.Pacific J. Math. 9 (1959), 1165-1177. Zbl 0087.04801, MR 0108570, 10.2140/pjm.1959.9.1165 |
Reference:
|
[15] J. Kisyński: Sur les familles compactes de fonctions mesurables.Colloq. Math. 7 (1960), 221-235. MR 0124459, 10.4064/cm-7-2-221-235 |
Reference:
|
[16] D. Maharam: An algebraic characterization of measure algebras.Annals of Math. 48 (1947), 154-167. Zbl 0029.20401, MR 0018718, 10.2307/1969222 |
Reference:
|
[17] T. Neubrunn, B. Riečan: Miera a Integrál.Bratislava, 1981, 485 - 497. MR 0657765 |
Reference:
|
[18] J. Niewiarowski: Convergence of sequences of real functions with respect to small systems.Math. Slov. 38 (1988), 333-340. Zbl 0659.28004, MR 0978763 |
Reference:
|
[19] K. Prikry: Changing measures into accessible cardinals.Dissert. Math. 68 (1970), 1-52. MR 0262075 |
Reference:
|
[20] K. Prikry: On measures on complete Boolean algebras.J. Symb. Logic 36 (1971), 395-406. MR 0297963, 10.2307/2269947 |
Reference:
|
[21] B. Riečan: Abstract formulation of some theorems of measure theory.Mat. Fyz. Časopis SAV 16 (1966), 268-273. MR 0222235 |
Reference:
|
[22] C. A. Rogers, J. E. Jayne: $K$-analytic sets.in: Analytic Sets (C. A. Rogers, J. E. Jayne, eds.), London, 1980, 1-181. |
Reference:
|
[23] D. A. Vladimirov: On the existence of invariant measures on Boolean algebras.Dokl. Akad. Nauk SSSR 157 (1964), 764-766. MR 0169985 |
Reference:
|
[24] D. A. Vladimirov: Invariant measures on Boolean algebras.Mat. Sb. (N.S.) 67 (109) (1965), 440-460. MR 0206206 |
Reference:
|
[25] E. Wajch: On small systems and compact families of Borel functions.Math. Slov. 40 (1990), 63-69. Zbl 0739.28002, MR 1094973 |
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