Nearly Hyperharmonic Functions are Infima of Excessive Functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10439109" target="_blank" >RIV/00216208:11320/20:10439109 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=OiaBIdHCmq" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=OiaBIdHCmq</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10959-019-00927-8" target="_blank" >10.1007/s10959-019-00927-8</a>
Alternative languages
Result language
angličtina
Original language name
Nearly Hyperharmonic Functions are Infima of Excessive Functions
Original language description
Let X be a Hunt process on a locally compact space X such that the set epsilon(X) of its Borel measurable excessive functions separates points, every function in epsilon(X) is the supremum of its continuous minorants in epsilon(X), and there are strictly positive continuous functions v, w is an element of epsilon(X) such that v/w vanishes at infinity. A numerical function u = 0 on X is said to be nearly hyperharmonic, if integral* u omicron X-tau V dP(x) <= u(x) for every x is an element of X and every relatively compact open neighborhood V of x, where tau(V) denotes the exit time of V. For every such function u, its lower semicontinuous regularization (u) over cap is excessive. The main purpose of the paper is to give a short, complete and understandable proof for the statement that u = inf{w is an element of epsilon(X) : w >= u} for every Borel measurable nearly hyperharmonic function on X. Principal novelties of our approach are the following: 1. A quick reduction to the special case, where starting at x is an element of X with u(x) < infinity the expected number of times the process X visits the set of points y. X, where <(u)over cap>(y) := lim inf(z) -> y u(z) < u(y), is finite. 2. The consequent use of (only) the strong Markov property. 3. The proof of the equality integral u d mu = inf{integral w d mu: w is an element of epsilon(X), w >= u} not only for measures mu satisfying integral w d mu < infinity for some excessive majorant w of u, but also for all finite measures. At the end, the measurability assumption on u is weakened considerably.
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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Theoretical Probability
ISSN
0894-9840
e-ISSN
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Volume of the periodical
33
Issue of the periodical within the volume
3
Country of publishing house
BE - BELGIUM
Number of pages
17
Pages from-to
1613-1629
UT code for WoS article
000550905100014
EID of the result in the Scopus database
2-s2.0-85068096128