---
res:
bibo_abstract:
- 'Let (X, H) be a P-harmonic space and assume for simplicity that constants are
harmonic. Given a numerical function phi on X which is locally lower bounded,
let J(phi) (x) := sup {integral* phi d mu : mu is an element of J(x) (X)}, x is
an element of X, where J(x) (X) denotes the set of all Jensen measures mu for
x, that is, mu is a compactly supported measure on X satisfying integral u d mu
<= u(x) for every hyperharmonic function u on X. The main purpose of the paper
is to show that, assuming quasi-universal measurability of phi, the function J(phi)
is the smallest nearly hyperharmonic function majorizing phi and that J(phi) =
phi boolean OR (J) over cap (phi), where (J) over cap (phi) J(phi) is the lower
semicontinuous regularization of J(phi). So, in particular, J(phi) turns out to
be at least "as measurable as" phi. This improves recent results, where the axiom
of polarity was assumed. The preliminaries on nearly hyperharmonic functions in
the framework of balayage spaces are closely related to the study of strongly
supermedian functions triggered by Mertens more than forty years ago.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Wolfhard
foaf_name: Hansen, Wolfhard
foaf_surname: Hansen
foaf_workInfoHomepage: http://www.librecat.org/personId=10524
- foaf_Person:
foaf_givenName: Ivan
foaf_name: Netuka, Ivan
foaf_surname: Netuka
bibo_doi: 10.5186/aasfm.2019.4401
bibo_volume: 44
dct_date: 2019^xs_gYear
dct_identifier:
- UT:000461094900001
dct_isPartOf:
- http://id.crossref.org/issn/1239-629X
- http://id.crossref.org/issn/1798-2383
dct_language: eng
dct_publisher: SUOMALAINEN TIEDEAKATEMIA@
dct_title: NEARLY HYPERHARMONIC FUNCTIONS AND JENSEN MEASURES@
...