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On integration in Banach spaces. VII. (English) Zbl 0674.28003

This part of author’s series dedicated to an integration theory for Banach space valued functions contains some complements and extensions of results from previous parts [especially Part III and Part V, same journal 29(104), 478-499 (1979; Zbl 0429.28011), ibid. 30(105), 610-628 (1980; Zbl 0506.28004), respectively] as well as connections with classical Kolmogorov integration theory and the work of M. Sion [“A theory of semigroup valued measures”, Lect. Notes Math. 355 (1973; Zbl 0312.28016)].
[For Part VI, same journal 35(110), 173-187 (1985) see Zbl 0628.28007.]
Reviewer: Gr.Arsene

MSC:

28B05 Vector-valued set functions, measures and integrals
46G10 Vector-valued measures and integration
28B10 Group- or semigroup-valued set functions, measures and integrals
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References:

[1] Bessaga C., Pelczyński A.: On bases and unconditional convergence of series in Banach spaces. Studia Math. 17 (1958), 151–164. · Zbl 0084.09805
[2] Bourbaki N.: Éléments de Mathématique, Livre VI, Integration. 2. éd. Chapter V, Hermann, Paris. · Zbl 0115.04903
[3] Brooks J. K., Dinculeanu N.: Lebesgue-type spaces for vector integration, linear operators, weak completeness and weak compactness. J. Math. Anal. Appl. 54, 1976, 348-389. · Zbl 0339.46029
[4] Day M. M.: Normed linear spaces. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. · Zbl 0082.10603
[5] Dobrakov I.: On integration in Banach spaces, I. Czech. Math. J. 20 (95), (1970), 511-536. · Zbl 0215.20103
[6] Dobrakov I.: On integration in Banach spaces, II. Czech. Math. J. 20 (95), (1970), 680-695. · Zbl 0224.46050
[7] Dobrakov I.: On integration in Banach spaces. III. Czech. Math. J. 29 (104), (1979), 478-499. · Zbl 0429.28011
[8] Dobrakov I.: On integration in Banach spaces, IV. Czech. Math. J. 30 (105), (1980), 259-279. · Zbl 0452.28006
[9] Dobrakov I.: On integration in Banach spaces, V. Czech. Math. J. 30 (105), (1980), 610-628. · Zbl 0506.28004
[10] Dobrakov I., Morales P.: On integration in Banach spaces, VI. Czech. Math. J. 35 (110), (1985), 173-187. · Zbl 0628.28007
[11] Dobrakov I.: On integration in Banach spaces, VIII (Polymeasures). Czech. Math. J. 37 (112), (1987), 487-506. · Zbl 0688.28002
[12] Dobrakov I.: On extension of vector polymeasures. Czech. Math. J. 38 (113), (1988), 88-94. · Zbl 0688.28005
[13] Dobrakov I.: Remarks on integrability in Banach spaces. Math. Slovaca 36, (1986), 323- 327. · Zbl 0635.28005
[14] Dunford N., Schwartz J. T.: Linear operators. Part I. Interscience, New York, 1958.
[15] Halmos P. R.: Measure theory. D. Van Nostrand, 1950. · Zbl 0040.16802
[16] Hille E., Phillips R.: Functional analysis and semigroups. Amer. Math. Soc. Coll. Publ., Providence, 1957. · Zbl 0078.10004
[17] Kolmogoroff A.: Untersuchungen über den Integralbegriff. Math. Ann. 103 (1930), 654-696. · JFM 56.0923.01
[18] Maynard H. B.: A general Radon-Nikodym theorem. Vector and operator valued mesures and applications. Academic Press, Inc. New York 1973, 233-246.
[19] Sion M.: A theory of semigroup valued measures. Lecture Notes Math., Vol. 355, Springer- Verlag, Berlin-Heidelberg-New York, 1973. · Zbl 0312.28016
[20] Swartz C.: Integrability for the Dobrakov integral. Czech. Math. J. 30 (105), (1980), 640-646. · Zbl 0506.28005
[21] Swartz C.: Weak Fubini theorems for the Dobrakov integral. Czech. Math. J. 30 (105), (1980), 647-654. · Zbl 0506.28006
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