Rao Chivukula, R.; Sastry, A. S. Product vector measures via Bartle integrals. (English) Zbl 0551.28009 J. Math. Anal. Appl. 96, 180-195 (1983). The authors consider the product of two measures with values in locally convex topological vector spaces X, Y, with respect to a given bilinear map \(X\times Y\to Z\), where Z is also a locally convex topological vector space. They prove also the existence of an integral representation of the product measure, which generalizes Bartle’s *-integral. This has been proved for measures fulfilling boundedness and absolute continuity conditions with respect to a positive finite measure. There are given comprehensive examples of measures which fail to have the latter property. Reviewer: P.Kruszynski Cited in 1 ReviewCited in 13 Documents MSC: 28B05 Vector-valued set functions, measures and integrals 28A35 Measures and integrals in product spaces 46G10 Vector-valued measures and integration Keywords:product of two measures with values in locally convex topological vector spaces; integral representation of the product measure; Bartle’s *- integral PDFBibTeX XMLCite \textit{R. Rao Chivukula} and \textit{A. S. Sastry}, J. Math. Anal. Appl. 96, 180--195 (1983; Zbl 0551.28009) Full Text: DOI References: [1] Bartle, R. G., A general bilinear vector integral, Studia Math., 15, 337-352 (1956) · Zbl 0070.28102 [2] Rao, M. Bhaskara, Countable additivity of a set function induced by two vector-valued measures, Indiana Univ. Math. J., 21, 847-848 (1972) · Zbl 0239.28002 [3] Dinculeanu, N., Vector Measures (1967), Pergamon: Pergamon New York [4] Dinculeanu, N.; Kluvanek, I., On vector measures, (Proc. London Math. Soc., 17 (1967)), 505-512 · Zbl 0195.34002 [5] Dobrakov, I., On integration in Banach spaces V, Czechoslovak Math. J., 30, 610-628 (1980) · Zbl 0506.28004 [6] Duchon, M., On the projective tensor product of vector valued measures II, Mat. Časopis Sloven. Akad. Vied., 19, 228-234 (1969) · Zbl 0188.20602 [7] Duchon, M.; Kluvanek, I., Inductive tensor product of vector-valued measures, Mat-Časopis Sloven. Akad. Vied., 17, 108-112 (1967) · Zbl 0162.19101 [8] Dudley, R. M.; Pakula, L., A counter-example on the inner product of measures, Indiana Univ. Math. J., 21, 843-845 (1972) · Zbl 0221.28003 [9] Grothendieck, A., Topological Vector Spaces (1973), Gordon & Breach: Gordon & Breach New York · Zbl 0275.46001 [10] Halmos, P. R., Measure Theory (1950), Van Nostrand: Van Nostrand New York · Zbl 0073.09302 [11] Horvath, J., Topological Vector Spaces and Distributions (1966), Addison-Wesley: Addison-Wesley London · Zbl 0143.15101 [12] Huneycutt, J. E., Products and convolutions of vector valued set functions, Studia Math., 41, 119-129 (1972) · Zbl 0233.28013 [13] Kluvanek, I.; Knowles, G., Vector Measures and Control Systems (1975), North-Holland: North-Holland Amsterdam [14] Saks, S., Addition to the note on some functionals, Trans. Amer. Math. Soc., 35, 967-974 (1933) · JFM 59.0428.11 [15] Sastry, A. S., Vector Integrals and Products of Vector Measures, (Ph. D. Thesis (1981), Univ. of Nebraska-Lincoln) · Zbl 0551.28009 [16] Swartz, C., Products of vector measures, Mat. Časopis Sloven. Akad. Vied., 24, 289-299 (1974) · Zbl 0291.28006 [17] Swartz, C., A generalization of a theorem of Duchon on products of vector measures, J. Math. Anal. Appl., 51, 621-628 (1975) · Zbl 0312.28015 [18] Thomas, G. E.F, The Lebesgue-Nikodym theorem for vector valued Radon measures, Mem. Amer. Math. Soc., 139 (1974) · Zbl 0282.28004 [19] Treves, F., Topological Vector Spaces, Distributions and Kernels (1967), Academic Press: Academic Press New York · Zbl 0171.10402 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.