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Sums of absolutely nonmeasurable functions
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Alexander Kharazishvili
Veröffentlicht/Copyright:
15. Mai 2013
Abstract.
Assuming Martin's Axiom, it is proved that every function acting from the real line ℝ into itself is representable as a sum of two absolutely nonmeasurable injective functions. A similar result is obtained for any endomorphism of the additive group ℝ.
Keywords: Absolutely nonmeasurable function; universal measure zero set; Martin's Axiom; generalized Luzin set
Received: 2011-06-23
Accepted: 2013-03-27
Published Online: 2013-05-15
Published in Print: 2013-05-01
© 2013 by Walter de Gruyter Berlin Boston
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- Coverings of internal groupoids and crossed modules in the category of groups with operations
- A new study on almost increasing and quasi-monotone sequences
- On precompact sets in spaces Cc(X)
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- Symmetry of an integral equation with Bessel potential in ℝn+
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- On the maximal operator of Marcinkiewicz–Fejér means of the two-dimensional Walsh–Kaczmarz system
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Schlagwörter für diesen Artikel
Absolutely nonmeasurable function;
universal measure zero set;
Martin's Axiom;
generalized Luzin set
Artikel in diesem Heft
- Masthead
- Fixed points of asymptotically regular mappings in complex-valued metric spaces
- Coverings of internal groupoids and crossed modules in the category of groups with operations
- A new study on almost increasing and quasi-monotone sequences
- On precompact sets in spaces Cc(X)
- Weighted boundedness for Toeplitz type operators related to Riesz transforms of the Schrödinger operator
- Sums of absolutely nonmeasurable functions
- Symmetry of an integral equation with Bessel potential in ℝn+
- Spanier spaces and the covering theory of non-homotopically path Hausdorff spaces
- On the maximal operator of Marcinkiewicz–Fejér means of the two-dimensional Walsh–Kaczmarz system
- Hofer type geometry on the space of Legendrian submanifolds of a contact manifold
- Initial problems for hyperbolic functional differential systems
- Approximation by complex q-Bernstein–Schurer operators in compact disks
- On some properties of conjugate trigonometric Fourier series
