Small systems -- on approximation of compact sets of measurable functions to compact subsets of $C_{c-o}(X)$
Czechoslovak Mathematical Journal, Tome 41 (1991) no. 4, pp. 619-633
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DOI : 10.21136/CMJ.1991.102494
Classification : 28A20, 54C50
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Wajch, Eliza. Small systems -- on approximation of compact sets of measurable functions to compact subsets of $C_{c-o}(X)$. Czechoslovak Mathematical Journal, Tome 41 (1991) no. 4, pp. 619-633. doi: 10.21136/CMJ.1991.102494

[1] D. K. Burke: Covering properties. in: Handbook of Set-Theoretic Topology (K. Kunen, J. E. Vaughan, eds.), North Holland-Amsterdam, 1984, 347-422. | MR | Zbl

[2] F. Cafiero: Misura e lntegrazione. Rome, 1959, 308-315.

[3] P. Capek: On small systems. Acta Fac. Rerum Natur. Univ. Comenian Math. 34 (1979), 93-101. | MR | Zbl

[4] G. Choquet: Forme abstraite du théorème de capacitabilité. Ann. Inst. Fourier 9 (1959), 83-89. | DOI | MR | Zbl

[5] R. Engelking: General Topology. Warsaw, 1977. | MR | Zbl

[6] M. Fréchet: Sur les ensembles compacts de fonctions measurables. Fund. Math. 9 (1927), 25-32. | DOI

[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. | MR | Zbl

[8] L. Gillman, M.Jerison: Rings of Continuous Functions. New York-Heidelberg-Berlin, 1976. | MR | Zbl

[9] E. H. Hanson: A note on compactness. Bull. Amer. Math. Soc. 39 (1933), 397-400. | DOI | MR | Zbl

[10] J. Hejduk, E. Wajch: Compactness in the sense of the convergence with respect to a small system. Math. Slov. 39 (1989), 267-275. | MR | Zbl

[11] A. Horn, A. Tarski: Measures in Boolean algebras. Trans. Amer. Math. Soc. 64 (1948), 467-497. | DOI | MR

[12] T. Jech: Set Theory. New York, 1978. | MR | Zbl

[13] R. A. Johnson J. Niewiarowski, T. Šwiątkowski: Small systems convergence and metrizability. Proc. Amer. Math. Soc. 103 (1988), 105-112. | DOI | MR

[14] J. L. Kelley: Measures on Boolean algebras. Pacific J. Math. 9 (1959), 1165-1177. | DOI | MR | Zbl

[15] J. Kisyński: Sur les familles compactes de fonctions mesurables. Colloq. Math. 7 (1960), 221-235. | DOI | MR

[16] D. Maharam: An algebraic characterization of measure algebras. Annals of Math. 48 (1947), 154-167. | DOI | MR | Zbl

[17] T. Neubrunn, B. Riečan: Miera a Integrál. Bratislava, 1981, 485 - 497. | MR

[18] J. Niewiarowski: Convergence of sequences of real functions with respect to small systems. Math. Slov. 38 (1988), 333-340. | MR | Zbl

[19] K. Prikry: Changing measures into accessible cardinals. Dissert. Math. 68 (1970), 1-52. | MR

[20] K. Prikry: On measures on complete Boolean algebras. J. Symb. Logic 36 (1971), 395-406. | DOI | MR

[21] B. Riečan: Abstract formulation of some theorems of measure theory. Mat. Fyz. Časopis SAV 16 (1966), 268-273. | MR

[22] C. A. Rogers, J. E. Jayne: $K$-analytic sets. in: Analytic Sets (C. A. Rogers, J. E. Jayne, eds.), London, 1980, 1-181.

[23] D. A. Vladimirov: On the existence of invariant measures on Boolean algebras. Dokl. Akad. Nauk SSSR 157 (1964), 764-766. | MR

[24] D. A. Vladimirov: Invariant measures on Boolean algebras. Mat. Sb. (N.S.) 67 (109) (1965), 440-460. | MR

[25] E. Wajch: On small systems and compact families of Borel functions. Math. Slov. 40 (1990), 63-69. | MR | Zbl

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