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On extension of vector polymeasures. II. (English) Zbl 0863.28005
Summary: We prove a necessary and sufficient condition for extension of a vector polymeasure from Cartesian product of rings to the Cartesian product of generated $$\sigma$$-rings.
[For Part I see Czech. Math. J. 38(113), No. 1, 88-94 (1988; Zbl 0688.28005)].

##### MSC:
 28B05 Vector-valued set functions, measures and integrals 46G10 Vector-valued measures and integration
##### Keywords:
extension; vector polymeasure
Full Text:
##### References:
 [1] DOBRAKOV, I: On integration in Banach space. VIII (Polymeasures), Czechoslovak Math. J. 37(112) (1987), 487-506. · Zbl 0688.28002 [2] DOBRAKOV, I: On extension of vector polymeasures. Czechoslovak Math. J. 38 (113) (1988), 88-94. · Zbl 0688.28005 [3] DOBRAKOV, I: On submeasures, I. Dissertationes Math. (Rozprawy Mat.) 112 (1974). · Zbl 0292.28001 [4] DOBRAKOV, I: Representation of multilinear operators on xCo(Ti), I. Czechoslovak Math. J. 39 (114) (1989), 288-302. · Zbl 0745.46048 [5] DOBRAKOV, I: Representation of multilinear operators on xCo(Ti,Ki). II. Atti Sem. Mat. Fis. Univ. Modena 42 (1994), 11-18. [6] HALMOS P. R.: Measure Theory. D. Van Nostrand, Toronto, 1950. · Zbl 0040.16802 [7] KLUVÁNEK, I: The extension and closure of vector measures. Vector and Operator Valued Measures and Aplications (D. H. Tucker and H. B. Maynard, Academic Press, Inc, New York-London, 1973, pp. 175-190.
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