Abstract:
The problem of general Radon representation is as follows. Given a Hausdorff topological space, find the space of linear functionals that are representable as integrals over all Radon measures. One of the possible solutions of this problem was obtained in Part I of this paper (see [39]). In Part II we establish that the classical theorems of Riesz–Radon and Prokhorov are corollaries of the theorem on general integral Radon representation proved in [39].
Citation:
V. K. Zakharov, A. V. Mikhalev, “The problem of general Radon representation for an arbitrary Hausdorff space. II”, Izv. Math., 66:6 (2002), 1087–1101
This publication is cited in the following 7 articles:
Machsoudi S., Rejali A., “on the Dual of Certain Locally Convex Function Spaces”, Bull. Iran Math. Soc., 41:4 (2015), 1003–1017
V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “Descriptive spaces and proper classes of functions”, J. Math. Sci., 213:2 (2016), 163–200
V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “Postclassical families of functions proper for descriptive and prescriptive spaces”, J. Math. Sci., 221:3 (2017), 360–383
V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “The characterization of integrals with respect to arbitrary Radon measures by the boundedness indices”, J. Math. Sci., 185:3 (2012), 417–429
V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “The Riesz–Radon–Fréchet problem of characterization of integrals”, Russian Math. Surveys, 65:4 (2010), 741–765
V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “Characterization of Radon integrals as linear functionals”, J. Math. Sci., 185:2 (2012), 233–281
V. K. Zakharov, “The Riesz–Radon Problem of Characterizing Integrals and the Weak Compactness of Radon Measures”, Proc. Steklov Inst. Math., 248 (2005), 101–110
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