# Lebesgue points for Sobolev functions on metric spaces.

Revista Matemática Iberoamericana (2002)

- Volume: 18, Issue: 3, page 685-700
- ISSN: 0213-2230

## Access Full Article

top## Abstract

top## How to cite

topKinnunen, Juha, and Latvala, Visa. "Lebesgue points for Sobolev functions on metric spaces.." Revista Matemática Iberoamericana 18.3 (2002): 685-700. <http://eudml.org/doc/39699>.

@article{Kinnunen2002,

abstract = {Our main objective is to study the pointwise behaviour of Sobolev functions on a metric measure space. We prove that a Sobolev function has Lebesgue points outside a set of capacity zero if the measure is doubling. This result seems to be new even for the weighted Sobolev spaces on Euclidean spaces. The crucial ingredient of our argument is a maximal function related to discrete convolution approximations. In particular, we do not use the Besicovitch covering theorem, extension theorems or representation formulas for Sobolev functions.},

author = {Kinnunen, Juha, Latvala, Visa},

journal = {Revista Matemática Iberoamericana},

keywords = {Espacios de funciones lineales; Espacios de Sobolev; Espacios métricos; Sobolev spaces; maximal functions; capacity},

language = {eng},

number = {3},

pages = {685-700},

title = {Lebesgue points for Sobolev functions on metric spaces.},

url = {http://eudml.org/doc/39699},

volume = {18},

year = {2002},

}

TY - JOUR

AU - Kinnunen, Juha

AU - Latvala, Visa

TI - Lebesgue points for Sobolev functions on metric spaces.

JO - Revista Matemática Iberoamericana

PY - 2002

VL - 18

IS - 3

SP - 685

EP - 700

AB - Our main objective is to study the pointwise behaviour of Sobolev functions on a metric measure space. We prove that a Sobolev function has Lebesgue points outside a set of capacity zero if the measure is doubling. This result seems to be new even for the weighted Sobolev spaces on Euclidean spaces. The crucial ingredient of our argument is a maximal function related to discrete convolution approximations. In particular, we do not use the Besicovitch covering theorem, extension theorems or representation formulas for Sobolev functions.

LA - eng

KW - Espacios de funciones lineales; Espacios de Sobolev; Espacios métricos; Sobolev spaces; maximal functions; capacity

UR - http://eudml.org/doc/39699

ER -

## Citations in EuDML Documents

top- Nijjwal Karak, Generalized Lebesgue points for Sobolev functions
- Malý, Jan, Coarea integration in metric spaces
- Takao Ohno, Tetsu Shimomura, Musielak-Orlicz-Sobolev spaces on metric measure spaces
- Takao Ohno, Tetsu Shimomura, Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.