On whitney-type characterization of approximate differentiability on metric measure spaces

E. Durand-Cartagena; L. Ihnatsyeva; R. Korte; M. Szumańska

doi:10.4153/CJM-2012-064-x

On whitney-type characterization of approximate differentiability on metric measure spaces

E. Durand-Cartagena, L. Ihnatsyeva, R. Korte, M. Szumańska

Not published at Aalto University

Research output: Contribution to journal › Article › Scientific › peer-review

2 Citations (Scopus)

Abstract

We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we prove a Stepanov-type theorem and consider approximate differentiability of Sobolev, BV, and maximal functions.

Original language	English
Pages (from-to)	721-742
Number of pages	22
Journal	Canadian Journal of Mathematics
Volume	66
Issue number	4
DOIs	https://doi.org/10.4153/CJM-2012-064-x
Publication status	Published - 1 Jan 2014
MoE publication type	A1 Journal article-refereed

Keywords

Approximate differentiability
Metric space
Strong measurable differentiable structure
Whitney theorem

Access to Document

10.4153/CJM-2012-064-x

Cite this

@article{51226ea56f2d43899599e36a46ff1661,

title = "On whitney-type characterization of approximate differentiability on metric measure spaces",

abstract = "We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we prove a Stepanov-type theorem and consider approximate differentiability of Sobolev, BV, and maximal functions.",

keywords = "Approximate differentiability, Metric space, Strong measurable differentiable structure, Whitney theorem",

author = "E. Durand-Cartagena and L. Ihnatsyeva and R. Korte and M. Szuma{\'n}ska",

year = "2014",

month = jan,

day = "1",

doi = "10.4153/CJM-2012-064-x",

language = "English",

volume = "66",

pages = "721--742",

journal = "Canadian Journal of Mathematics",

issn = "0008-414X",

publisher = "Canadian Mathematical Society",

number = "4",

}

TY - JOUR

T1 - On whitney-type characterization of approximate differentiability on metric measure spaces

AU - Durand-Cartagena, E.

AU - Ihnatsyeva, L.

AU - Korte, R.

AU - Szumańska, M.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we prove a Stepanov-type theorem and consider approximate differentiability of Sobolev, BV, and maximal functions.

AB - We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we prove a Stepanov-type theorem and consider approximate differentiability of Sobolev, BV, and maximal functions.

KW - Approximate differentiability

KW - Metric space

KW - Strong measurable differentiable structure

KW - Whitney theorem

UR - http://www.scopus.com/inward/record.url?scp=84906655323&partnerID=8YFLogxK

U2 - 10.4153/CJM-2012-064-x

DO - 10.4153/CJM-2012-064-x

M3 - Article

AN - SCOPUS:84906655323

SN - 0008-414X

VL - 66

SP - 721

EP - 742

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

IS - 4

ER -

On whitney-type characterization of approximate differentiability on metric measure spaces

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this