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ON SEPARABLE SUPPORTS OF BOREL MEASURES
"... Abstract. Some properties of Borel measures with separable supports are considered. In particular, it is proved that any σfinite Borel measure on a Suslin line has a separable supports and from this fact it is deduced, using the continuum hypothesis, that any Suslin line contains a Luzin subspace w ..."
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Abstract. Some properties of Borel measures with separable supports are considered. In particular, it is proved that any σfinite Borel measure on a Suslin line has a separable supports and from this fact it is deduced, using the continuum hypothesis, that any Suslin line contains a Luzin subspace
Effective Borel measurability and reducibility of functions
 Mathematical Logic Quarterly
"... The investigation of computational properties of discontinuous functions is an important concern in computable analysis. One method to deal with this subject is to consider effective variants of Borel measurable functions. We introduce such a notion of Borel computability for singlevalued as well ..."
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Cited by 34 (9 self)
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The investigation of computational properties of discontinuous functions is an important concern in computable analysis. One method to deal with this subject is to consider effective variants of Borel measurable functions. We introduce such a notion of Borel computability for singlevalued as well
Duality for borel measurable cost function
"... measure theoretic setting. Our main result states that duality holds if c: X × Y → [0, ∞) is an arbitrary Borel measurable cost function on the product of Polish spaces X, Y. In the course of the proof we show how to relate a non optimal transport plan to the optimal transport costs via a “subsidy ..."
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Cited by 13 (4 self)
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measure theoretic setting. Our main result states that duality holds if c: X × Y → [0, ∞) is an arbitrary Borel measurable cost function on the product of Polish spaces X, Y. In the course of the proof we show how to relate a non optimal transport plan to the optimal transport costs via a “subsidy
Moderation of sigmafinite Borel measures
, 1997
"... We establish that a σfinite Borel measure µ in a Hausdorff topological space X such that each open subset of X is µRadon, is moderated when X is weakly metacompact or paralindelöf and also when X is metalindelöf and has a µconcassage of separable subsets. Moreover, we give a new proof of a theo ..."
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We establish that a σfinite Borel measure µ in a Hausdorff topological space X such that each open subset of X is µRadon, is moderated when X is weakly metacompact or paralindelöf and also when X is metalindelöf and has a µconcassage of separable subsets. Moreover, we give a new proof of a
Borel measurable functionals on measure algebras
, 2010
"... Let A be a Banach algebra. Then there are two natural products, here denoted by □ and ♦, on the second dual A ′ ′ of A; they are the Arens products. For definitions and discussions of these products, see [3, 4, 5, 6], for example. We briefly recall the definitions. As usual, A ′ and A ′ ′ are Banach ..."
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∗algebra is Arens regular. Recently, the three participants have studied [5] the second dual of a semigroup algebra; here S is a semigroup, and our Banach algebra is A = (ℓ 1 (S), ⋆). We see that the second dual A ′ ′ can be identified with the space M(βS) of complexvalued, regular Borel measures on β
An Uncountable Family of Regular Borel measures
, 2007
"... ABSTRACT. Let c> 0 be a fixed constant. Let 0 ≤ r < s be an arbitrary pair of real numbers. Let a, b be any pair of real numbers such that  b − a  ≤ c(s − r). Define C s r to be the set of continuous realvalued functions on [r, s], and define Cr to be the set of continuous realvalued func ..."
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∈ Λ s r  x(r) = a}, (4) Λ s,b r = { x ∈ Λsr  x(s) = b}, (5) Λr,a = { x ∈ Λr  x(r) = a}. (6) We present a general method of constructing an uncountable family of regular Borel measures on each of the sets (1), (2), and an uncountable family of regular Borel probability measures on each
Measurability Of Some Sets Of Borel Measurable Functions On
, 247
"... . In the paper we show that the space of injective Borel measurable functions and the space of functions, which norm attains supremum at exactly one point, with supremum metric are coanalyticly hard by using the space of trees. In this paper we show that the set of injective functions is not Suslin ..."
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. In the paper we show that the space of injective Borel measurable functions and the space of functions, which norm attains supremum at exactly one point, with supremum metric are coanalyticly hard by using the space of trees. In this paper we show that the set of injective functions is not Suslin
LATTICEVALUED BOREL MEASURES III
"... Abstract. Let X be a completely regular T1 space, E a boundedly complete vector lattice, C(X) (Cb(X)) the space of all (all, bounded), realvalued continuous functions on X. In order convergence, we consider Evalued, orderbounded, σadditive, τadditive, and tight measures on X and prove some orde ..."
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Abstract. Let X be a completely regular T1 space, E a boundedly complete vector lattice, C(X) (Cb(X)) the space of all (all, bounded), realvalued continuous functions on X. In order convergence, we consider Evalued, orderbounded, σadditive, τadditive, and tight measures on X and prove some
Measurability of Some Sets of Borel Measurable Functions on [0,1]
, 1995
"... In the paper we show that the space of injective Borel measurable functions and the space of functions, which norm attains supremum at exactly one point, with supremum metric are coanalyticly hard by using the space of trees. ..."
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In the paper we show that the space of injective Borel measurable functions and the space of functions, which norm attains supremum at exactly one point, with supremum metric are coanalyticly hard by using the space of trees.
Results 1  10
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59,297