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Strong additivity, absolute continuity, and compactness in spaces of measures. (English) Zbl 0284.28005


MSC:

28B05 Vector-valued set functions, measures and integrals
46G10 Vector-valued measures and integration
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References:

[1] Bartle, R. G.; Dunford, N.; Schwartz, J., Weak compactness and vector measures, Canad. J. Math., 7, 289-305 (1955) · Zbl 0068.09301
[2] Brooks, J. K., On the existence of a control measure for strongly bounded vector measures, Bull. Amer. Math. Soc., 77, 999-1001 (1971) · Zbl 0229.28008
[3] Brooks, J. K., Weak compactness in the space of vector measures, Bull. Amer. Math. Soc., 78, 284-287 (1972) · Zbl 0241.28011
[4] Brooks, J. K., On compactness of measures, Bull. Acad. Pol. Sci., Ser. Sci. Math. Astron. Phys., 20, 991-994 (1972) · Zbl 0244.46048
[5] Brooks, J. K., Equicontinuous sets of measures and applications to Vitali’s integral convergence theorem and control measures, Advances in Math., 10, 165-171 (1973) · Zbl 0249.28009
[6] J. K. Brooks; J. K. Brooks · Zbl 0294.28008
[7] J. K. Brooks; J. K. Brooks
[8] Brooks, J. K.; Dinculeanu, N., Weak compactness and control measures in the space of unbounded measures, (Proc. Nat. Acad. Sci., 69 (1972)), 1083-1085 · Zbl 0238.28002
[9] Brooks, J. K.; Dinculeanu, N., Critères de compacité dans les espaces de mesures vectorielles, C. R. Acad. Sci. Paris, 274, 1627-1628 (1972) · Zbl 0238.28003
[10] Brooks, J. K.; Jewett, R. S., On finitely additive vector measures, (Proc. Nat. Acad. Sci., 67 (1970)), 1294-1298 · Zbl 0216.09602
[11] J. K. Brooks and H. S. Walker; J. K. Brooks and H. S. Walker
[12] Brooks, J. K.; Lewis, P. W., Operators on function spaces, Bull. Amer. Math. Soc., 78, 697-701 (1972) · Zbl 0265.47021
[13] J. K. Brooks and P. W. LewisTrans. Amer. Math. Soc.; J. K. Brooks and P. W. LewisTrans. Amer. Math. Soc.
[14] Dieudonné, J., Sur les espaces de Köthe, J. Analyse Math., 1, 81-115 (1951) · Zbl 0044.11703
[15] Diestel, J., Applications of weak compactness and bases to vector measures and vectorial integration, Rev. Roumaine Math. Pures Appl., 18, 211-224 (1973) · Zbl 0267.46035
[16] Dinculeanu, N., Vector Measures (1967), Pergamon Press: Pergamon Press Oxford
[17] Dinculeanu, N.; Uhl, J. J., A unifying Radon-Nikodym theorem for vector measures, J. Multivariate Analysis, 3, 184-203 (1973) · Zbl 0283.60051
[18] Dunford, N.; Pettis, B. J., Linear operations on summable functions, Trans. Amer. Math. Soc., 47, 323-392 (1940) · Zbl 0023.32902
[19] Dunford, N.; Schwartz, J. T., Linear Operators (1958), Interscience: Interscience New York, Part I
[20] Grothendieck, A., Sur les applications linéaires faiblement compactes d’espaces du type \(C(K)\), Canad. J. Math., 5, 129-173 (1953) · Zbl 0050.10902
[21] Lewis, D., Conditional weak compactness in certain injective tensor products, Math. Ann., 201, 201-209 (1973) · Zbl 0234.46069
[22] Pettis, B. J., On integration in vector spaces, Trans. Amer. Math. Soc., 44, 277-304 (1938) · Zbl 0019.41603
[23] Phillips, R. S., On weakly compact subsets of a Banach space, Amer. J. Math., 65, 108-136 (1943) · Zbl 0063.06212
[24] Phillips, R. S., On linear transformations, Trans. Amer. Math. Soc., 48, 516-541 (1940) · Zbl 0025.34202
[25] Rickart, C. E., Decomposition of additive set functions, Duke Math. J., 10, 653-665 (1943) · Zbl 0063.06492
[26] Thorp, E. O.; Whitley, R. J., Operator representation theorems, Ill. Math. J., 9, 595-601 (1965) · Zbl 0133.07103
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