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Integration with vector valued measures
Discrete and Continuous Dynamical Systems, 2013 Of the many variations of vector measures, the Frechet variation is finite valued but only subadditive. Finding a `controlling' finite measure for these in several cases, it is possible to develop a useful integration of the Bartle-Dunford-Schwartz type for many linear metric spaces. These include the generalized Orlicz spaces, $L^{\varphi}(\mu)$,
M M Rao
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On the theory of vector valued Loeb measures and integration
Journal of Functional Analysis, 1992 The author generalizes the construction of the Loeb measure associated to an internal measure space to the case, where the internal measure takes values in an internal Banach space. He develops a corresponding integration theory. Finally he gives two interesting applications to the standard theory of Banach space-valued measures: The first one is the ...
Yeneng Sun
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Vector valued information measures and integration with respect to fuzzy vector capacities
Fuzzy Sets and Systems, 2019 [EN] Integration with respect to vector-valued fuzzy measures is used to define and study information measuring tools. Motivated by some current developments in Information Science, we apply the integration of scalar functions with respect to vector-valued fuzzy measures, also called vector capacities.
Enrique Alfonso Sánchez Perez
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Integration of vector-valued functions with respect to vector measures defined on $δ$-rings
Illinois Journal of Mathematics, 2011 This paper extends the theory of scalar-valued integrable functions with respect to vector measures defined on $δ$-rings to the case of vector-valued tensor integrable functions with respect to vector measures defined on $δ$-rings. This paper also generalizes some results of G. F. Stefansson for tensor integration theory of vector-valued functions with
Chakraborty, N. D., Basu, Santwana
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Homogeneous Banach Spaces as Banach Convolution Modules over M(G)
Mathematics, 2022 This paper is supposed to form a keystone towards a new and alternative approach to Fourier analysis over LCA (locally compact Abelian) groups G.
Hans Georg Feichtinger
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Journal of Function Spaces, 2020 The aim of this study is to generalize moving average by means of Choquet integral. First, by employing nonadditive measures with δ − λ rules, the calculation of the moving average for a series of fuzzy numbers can be transformed into Choquet integration
Zengtai Gong +3 more
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Integration of vector-valued functions with respect to an operator-valued measure [PDF]
Czechoslovak Mathematical Journal, 1986 The authors develop an integration theory as indicated in the title which generalizes some previous work to a locally convex space setting [see e.g. \textit{C. Debieve}, Rev. Roum. Math. Pures Appl. 26, 943-957 (1981; Zbl 0463.46038), \textit{I. Dobrakov}, Czech. Math. J. 20(95), 511-536 (1970; Zbl 0215.201), and \textit{A.
Roy, S. K., Chakraborty, N. D.
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Interchange of vector valued integrals when the measures are Bochner or Pettis indefinite integrals [PDF]
Bulletin of the Australian Mathematical Society, 1979 Necessary and sufficient conditions for the interchange of two Bochner integrals and for the interchange of two Pettis integrals are obtained. These conditions are different from those generally required in classical Fubini theorems since they do not require the construction of the cross product measure.
De Korvin, Andre +1 more
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Singular Bilinear Integrals in Quantum Physics
Mathematics, 2015 Bilinear integrals of operator-valued functions with respect to spectral measures and integrals of scalar functions with respect to the product of two spectral measures arise in many problems in scattering theory and spectral analysis. Unfortunately, the
Brian Jefferies
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Vector valued Loeb measures and the Lewis integral.
MATHEMATICA SCANDINAVICA, 1991 The author presents a very comprehensive account of the theory of internal vector-valued set functions and the vector-valued Loeb measures they generate. As examples, the author discusses the scalar-valued Loeb measures, measures valued in internal Banach spaces and measures with values in non-standard hulls.
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