On Evans' and Choquet's Theorems for Polar Sets
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10456814" target="_blank" >RIV/00216208:11320/22:10456814 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=eobt-LVf3V" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=eobt-LVf3V</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11118-020-09890-0" target="_blank" >10.1007/s11118-020-09890-0</a>
Alternative languages
Result language
angličtina
Original language name
On Evans' and Choquet's Theorems for Polar Sets
Original language description
By classical results of G.C. Evans and G. Choquet on "good" kernels G in potential theory, for every polar Kσ-set P, there exists a finite measure μ on P such that its potential Gμ is infinite on P, and a set P admits a finite measure μ on P such that Gμ is infinite exactly on P if and only if P is a polar Gδ-set. A known application of Evans' theorem yields the solutions of the generalized Dirichlet problem for open sets by the Perron-Wiener-Brelot method using only harmonic upper and lower functions. It is shown that, by an elementary "metric sweeping" of measures and without using any potential theory, such results can be obtained for general kernels G satisfying a local triangle property, a property which amounts to G being locally equivalent to some negative power of some metric. The particular case, G(x,y) = |x - y|α-d on Rd, 2 < α < d, solves a long-standing open problem.
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
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Potential Analysis [online]
ISSN
1572-929X
e-ISSN
1572-929X
Volume of the periodical
56
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
13
Pages from-to
423-435
UT code for WoS article
000622251400001
EID of the result in the Scopus database
2-s2.0-85101996610