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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) &lt; 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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

  • 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

  • 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