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The Banach-Zarecki theorem for functions with values in metric spaces
Author(s):
Jakub
Duda;
Ludek
Zajícek
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3631-3633.
MSC (2000):
Primary 26A46;
Secondary 26E20
Posted:
June 3, 2005
MathSciNet review:
2163600
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Abstract:
Using an old result of Luzin about his property  , we prove a general version of the Banach-Zarecki theorem (on absolute continuity and Luzin's property  ).
References:
-
- [BL]
- Y. Benyamini, J. Lindenstrauss, Geometric Nonlinear Functional Analysis, Vol. 1, Colloquium Publications 48, American Mathematical Society, Providence, 2000. MR 1727673 (2001b:46001)
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- H. Federer, Geometric Measure Theory, Grundlehren der math. Wiss., vol. 153, Springer, New York, 1969. MR 0257325 (41:1976)
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- J. Foran, A note on Lusin's condition
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- P. Holický, S. P. Ponomarev, L. Zajícek, M. Zelený, Structure of the set of continuous functions with Luzin's property (N), Real Anal. Exchange 24 (1998/99), no. 2, 635-656. MR 1704740 (2000k:28002)
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- N. Luzin, The Integral and Trigonometric Series (Russian), Moskva, Mat. Sborn. 30 (1916), 1-242 (enhanced ed., Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad, 1951). MR 0048364 (14:2g)
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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:
10.1090/S0002-9939-05-07959-1
PII:
S 0002-9939(05)07959-1
Keywords:
Absolutely continuous functions,
Luzin's property $(N)$,
Banach-Zarecki Theorem
Received by editor(s):
August 17, 2004
Posted:
June 3, 2005
Additional Notes:
The first author was supported by the grant GACR 201/03/0931.
The second author was supported by the grants MSM 113200007 and GACR 201/03/0931.
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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