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Removal Lemma for null sets

by n.n. , 2013
"... The Removal Lemma (more generally, the Alon–Shapira Theorem 15.24) has a graphon analogue, where instead of talking about sets of small measure, we talk about nullsets. Besides the version stated and proved below, such analogues were given by Svante Janson ([3], Lemma 5.3) and more recently by Fedor ..."
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The Removal Lemma (more generally, the Alon–Shapira Theorem 15.24) has a graphon analogue, where instead of talking about sets of small measure, we talk about nullsets. Besides the version stated and proved below, such analogues were given by Svante Janson ([3], Lemma 5.3) and more recently

Haar null sets and the consistent . . .

by Márton Elekes , et al. , 2011
"... ..."
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Null sets and games in . . .

by Jakub Duda, et al. - TOPOLOGY AND ITS APPLICATIONS 156 (2008) 56–60 , 2008
"... ..."
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On covering of real line by null sets

by Tomek Bartoszynski, Tomek Bartoszynski - Pacific Journal of Mathematics , 1988
"... In this note it is proved that the least cardinal K such that R cannot be covered by fc many null sets cannot have countable cofinality, provided 2ω-scale exists and 2ω is regular cardinal. Using the same assumption a combinatorial characterisation of this cardinal is also found. Let κ m be the leas ..."
Abstract - Cited by 8 (1 self) - Add to MetaCart
In this note it is proved that the least cardinal K such that R cannot be covered by fc many null sets cannot have countable cofinality, provided 2ω-scale exists and 2ω is regular cardinal. Using the same assumption a combinatorial characterisation of this cardinal is also found. Let κ m

EVERYWHERE MEAGRE AND EVERYWHERE NULL SETS

by Jan Kraszewski
"... We introduce new classes of small subsets of the reals, having natural combinatorial definitions, namely everywhere meagre and everywhere null sets. We investigate properties of these sets, in particular we show that these classes are closed under taking products and projections. We also prove sev ..."
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We introduce new classes of small subsets of the reals, having natural combinatorial definitions, namely everywhere meagre and everywhere null sets. We investigate properties of these sets, in particular we show that these classes are closed under taking products and projections. We also prove

Haar null sets without Gδ hulls

by Márton Elekes , et al. , 2014
"... Let G be an abelian Polish group, e.g. a separable Banach space. A subset X ⊂ G is called Haar null (in the sense of Christensen) if there exists a Borel set B ⊃ X and a Borel probability measure µ on G such that µ(B+g) = 0 for every g ∈ G. The term shy is also commonly used for Haar null, and co-H ..."
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Let G be an abelian Polish group, e.g. a separable Banach space. A subset X ⊂ G is called Haar null (in the sense of Christensen) if there exists a Borel set B ⊃ X and a Borel probability measure µ on G such that µ(B+g) = 0 for every g ∈ G. The term shy is also commonly used for Haar null, and co

Comparing the uniformity invariants of null sets . . .

by Saharon Shelah, et al. , 2004
"... It is shown to be consistent with set theory that the uniformity invariant for Lebesgue measure is strictly greater than the corresponding invariant for Hausdorff r-dimensional measure where 0 < r < 1. ..."
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It is shown to be consistent with set theory that the uniformity invariant for Lebesgue measure is strictly greater than the corresponding invariant for Hausdorff r-dimensional measure where 0 < r < 1.

THE STEINHAUS PROPERTY AND HAAR-NULL SETS

by Pandelis Dodos , 2010
"... ..."
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Comparing the uniformity invariants of null sets . . .

by Philippe Gaucher , 2003
"... A functor is constructed from the category of globular CW-complexes to that of flows. It allows to compare the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, one proves that t ..."
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A functor is constructed from the category of globular CW-complexes to that of flows. It allows to compare the S-homotopy equivalences (resp. the T-homotopy equivalences) of globular complexes with the S-homotopy equivalences (resp. the T-homotopy equivalences) of flows. Moreover, one proves that this functor induces an equivalence of categories from the localization of the category of globular CW-complexes with respect to S-homotopy equivalences to the localization of the category of flows with respect to weak

Null sets and essentially smooth Lipschitz functions

by Jonathan M. Borwein, Warren B. Moors - SIAM J. Optim , 1997
"... In this paper we extend the notion of a Lebesgue-null set to a notion which is valid in any completely metrizable Abelian topological group. We then use this definition to introduce and study the class of essentially smooth functions. These are, roughly speaking, those Lipschitz functions which are ..."
Abstract - Cited by 12 (10 self) - Add to MetaCart
In this paper we extend the notion of a Lebesgue-null set to a notion which is valid in any completely metrizable Abelian topological group. We then use this definition to introduce and study the class of essentially smooth functions. These are, roughly speaking, those Lipschitz functions which
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