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Removal Lemma for null sets
, 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
On covering of real line by null sets
 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 2ωscale 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 ..."
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Cited by 8 (1 self)
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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 2ωscale 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
"... 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
, 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 coH ..."
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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 . . .
, 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 rdimensional 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 rdimensional measure where 0 < r < 1.
Comparing the uniformity invariants of null sets . . .
, 2003
"... A functor is constructed from the category of globular CWcomplexes to that of flows. It allows to compare the Shomotopy equivalences (resp. the Thomotopy equivalences) of globular complexes with the Shomotopy equivalences (resp. the Thomotopy equivalences) of flows. Moreover, one proves that t ..."
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A functor is constructed from the category of globular CWcomplexes to that of flows. It allows to compare the Shomotopy equivalences (resp. the Thomotopy equivalences) of globular complexes with the Shomotopy equivalences (resp. the Thomotopy equivalences) of flows. Moreover, one proves that this functor induces an equivalence of categories from the localization of the category of globular CWcomplexes with respect to Shomotopy equivalences to the localization of the category of flows with respect to weak
Null sets and essentially smooth Lipschitz functions
 SIAM J. Optim
, 1997
"... In this paper we extend the notion of a Lebesguenull 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 ..."
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Cited by 12 (10 self)
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In this paper we extend the notion of a Lebesguenull 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
Results 1  10
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2,636