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The Banach-Zarecki theorem for functions with values in metric spaces


Authors: Jakub Duda and Ludek Zajícek
Journal: Proc. Amer. Math. Soc. 133 (2005), 3631-3633
MSC (2000): Primary 26A46; Secondary 26E20
DOI: https://doi.org/10.1090/S0002-9939-05-07959-1
Published electronically: June 3, 2005
MathSciNet review: 2163600
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Abstract: Using an old result of Luzin about his property $(N)$, we prove a general version of the Banach-Zarecki theorem (on absolute continuity and Luzin's property $(N)$).


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Additional Information

Jakub Duda
Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
Email: jakub.duda@weizmann.ac.il

Ludek Zajícek
Affiliation: Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email: zajicek@karlin.mff.cuni.cz

DOI: https://doi.org/10.1090/S0002-9939-05-07959-1
Keywords: Absolutely continuous functions, Luzin's property $(N)$, Banach-Zarecki Theorem
Received by editor(s): August 17, 2004
Published electronically: June 3, 2005
Additional Notes: The first author was supported by the grant GAČR 201/03/0931.
The second author was supported by the grants MSM 113200007 and GAČR 201/03/0931.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.