Reduced functions and Jensen measures

Hansen W, Netuka I (2018)
Proceedings of the American Mathematical Society 146(1): 153-160.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor*in
Hansen, WolfhardUniBi; Netuka, Ivan
Abstract / Bemerkung
Let phi be a locally upper bounded Borel measurable function on a Greenian open set Omega in R-d and, for every x is an element of Omega, let v(phi)( x) denote the infimum of the integrals of phi with respect to Jensen measures for x on Omega. Twenty years ago, B.J. Cole and T.J. Ransford proved that v(phi) is the supremum of all subharmonic minorants of phi on X and that the sets {v(phi) < t}, t is an element of R, are analytic. In this paper, a different method leading to the inf-supresult establishes at the same time that, in fact, v(phi) is the minimum of phi and a subharmonic function, and hence Borel measurable. This is presented in the generality of harmonic spaces, where semipolar sets are polar, and the key tools are measurability results for reduced functions on balayage spaces which are of independent interest.
Stichworte
Reduced function; Jensen measure; axiom of polarity
Erscheinungsjahr
2018
Zeitschriftentitel
Proceedings of the American Mathematical Society
Band
146
Ausgabe
1
Seite(n)
153-160
ISSN
0002-9939
eISSN
1088-6826
Page URI
https://pub.uni-bielefeld.de/record/2916106

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Hansen W, Netuka I. Reduced functions and Jensen measures. Proceedings of the American Mathematical Society. 2018;146(1):153-160.
Hansen, W., & Netuka, I. (2018). Reduced functions and Jensen measures. Proceedings of the American Mathematical Society, 146(1), 153-160. doi:10.1090/proc/13688
Hansen, W., and Netuka, I. (2018). Reduced functions and Jensen measures. Proceedings of the American Mathematical Society 146, 153-160.
Hansen, W., & Netuka, I., 2018. Reduced functions and Jensen measures. Proceedings of the American Mathematical Society, 146(1), p 153-160.
W. Hansen and I. Netuka, “Reduced functions and Jensen measures”, Proceedings of the American Mathematical Society, vol. 146, 2018, pp. 153-160.
Hansen, W., Netuka, I.: Reduced functions and Jensen measures. Proceedings of the American Mathematical Society. 146, 153-160 (2018).
Hansen, Wolfhard, and Netuka, Ivan. “Reduced functions and Jensen measures”. Proceedings of the American Mathematical Society 146.1 (2018): 153-160.