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Rectifiability of the jump set of locally integrable functions

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Del Nin, Giacomo (2021) Rectifiability of the jump set of locally integrable functions. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 22 (3). pp. 1233-1240. doi:10.2422/2036-2145.202002_006 ISSN 0391-173X.

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Official URL: http://dx.doi.org/10.2422/2036-2145.202002_006

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Abstract

In this note we show that for every measurable function on Rn the set
of points where the blowup exists and is not constant is (n 1)-rectifiable. In particular, for every u 2 L1 loc(Rn) the jump set Ju is (n 1)-rectifiable.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Functions, Entire, Functions of bounded variation, Hausdorff measures
Journal or Publication Title: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
Publisher: Scuola Normale Superiore di Pisa
ISSN: 0391-173X
Official Date: 27 September 2021
Dates:
DateEvent
27 September 2021Published
24 April 2020Accepted
Volume: 22
Number: 3
Page Range: pp. 1233-1240
DOI: 10.2422/2036-2145.202002_006
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 27 July 2021
Date of first compliant Open Access: 27 July 2021
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