Results 21 to 30 of about 88,517 (218)
Journal of Mathematics, 2016 In this paper, a graph is assigned to any probability measure on the σ-algebra of Borel sets of a topological space. Using this construction, it is proved that given any number n (finite or infinite) there exists a nonregular graph such that its clique ...
A. Assari, M. Rahimi
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Identifying 1-rectifiable measures in Carnot groups
Analysis and Geometry in Metric Spaces, 2023 We continue to develop a program in geometric measure theory that seeks to identify how measures in a space interact with canonical families of sets in the space. In particular, extending a theorem of M. Badger and R.
Badger Matthew, Li Sean, Zimmerman Scott
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Borel complexity of sets of normal numbers via generic points in subshifts with specification
, 2020 We study the Borel complexity of sets of normal numbers in several numeration systems. Taking a dynamical point of view, we offer a unified treatment for continued fraction expansions and base $r$ expansions, and their various generalisations ...
Airey, Dylan +3 more
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Turning Borel sets into clopen sets effectively
, 2012 We present the effective version of the theorem about turning Borel sets in Polish spaces into clopen sets while preserving the Borel structure of the underlying space.
Gregoriades, Vassilios
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Borel structures on the set of Borel mappings
Topology and its Applications, 2012 In the paper [Pac. J. Math. 1, 5--31 (1951; Zbl 0044.11801)], \textit{R. Arens} and \textit{J. Dugundji} introduced and studied several types of topologies on the spaces of continuous functions such as admissible, proper and splitting topologies. In the paper under review, the authors study analogously Borel splitting and admissible structures on the ...
Georgiou, Dimitris +2 more
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On existence of the support of a Borel measure
Demonstratio Mathematica, 2018 We present arguments showing that the standard notion of the support of a probabilistic Borel measure is not well defined in every topological space. Our goal is to create a “very inseparable” space and to show the existence of a family of closed sets ...
Kozarzewski Piotr A.
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Events of Borel Sets, Construction of Borel Sets and Random Variables for Stochastic Finance [PDF]
Formalized Mathematics, 2014 Summary We consider special events of Borel sets with the aim to prove, that the set of the irrational numbers is an event of the Borel sets. The set of the natural numbers, the set of the integer numbers and the set of the rational numbers are countable, so we can use the literature [10] (pp.
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About Some Monge–Kantovorich Type Norm and Their Applications to the Theory of Fractals
Mathematics, 2022 If X is a Hilbert space, one can consider the space cabv(X) of X valued measures defined on the Borel sets of a compact metric space, having a bounded variation. On this vector measures space was already introduced a Monge–Kantorovich type norm.
Ion Mierluș-Mazilu, Lucian Niță
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Forcing properties of ideals of closed sets
, 2010 With every $\sigma$-ideal $I$ on a Polish space we associate the $\sigma$-ideal $I^*$ generated by the closed sets in $I$. We study the forcing notions of Borel sets modulo the respective $\sigma$-ideals $I$ and $I^*$ and find connections between their ...
Sabok, Marcin, Zapletal, Jindrich
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On the sum of two Borel sets [PDF]
Proceedings of the American Mathematical Society, 1970 It is shown that the linear sum of two Borel subsets of the real line need not be Borel, even if one of them is compact and the other is \(G_\delta\). This result is extended to a fairly wide class of connected topological groups.
Erdős, Pál, Stone, A. H.
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