AM-modulus and Hausdorff measure of codimension one in metric measure spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10456734" target="_blank" >RIV/00216208:11320/22:10456734 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ORXhg6A3a3" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ORXhg6A3a3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.202000059" target="_blank" >10.1002/mana.202000059</a>

Result language
angličtina
Original language name
AM-modulus and Hausdorff measure of codimension one in metric measure spaces
Original language description
Let Gamma(E) be the family of all paths which meet a set E in the metric measure space X. The set function E bar right arrow AM (Gamma(E)) defines the AM-modulus measure in X where AM refers to the approximation modulus [22]. We compare AM (Gamma(E)) to the Hausdorff measure coH(1) (E) of codimension one in X and show that coH(1)(E) approximate to AM(Gamma(E)) for Suslin sets E in X. This leads to a new characterization of sets of finite perimeter in X in terms of the AM-modulus. We also study the level sets of BV functions and show that for a.e. t. these sets have finite coH(1)-measure. Most of the results are new also in R-n.
Czech name
—
Czech description
—

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

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)