Reduced functions and Jensen measures
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10369671" target="_blank" >RIV/00216208:11320/18:10369671 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1090/proc/13688" target="_blank" >http://dx.doi.org/10.1090/proc/13688</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/13688" target="_blank" >10.1090/proc/13688</a>
Alternative languages
Result language
angličtina
Original language name
Reduced functions and Jensen measures
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the American Mathematical Society
ISSN
0002-9939
e-ISSN
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Volume of the periodical
146
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
8
Pages from-to
153-160
UT code for WoS article
000415212000014
EID of the result in the Scopus database
2-s2.0-85034220417