Metrically generated probabilistic metric spaces
R. Stevens (1967)
Fundamenta Mathematicae
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R. Stevens (1967)
Fundamenta Mathematicae
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Ralph Raimi (1967)
Fundamenta Mathematicae
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Roman Duda, Rastislav Telgársky (1968)
Czechoslovak Mathematical Journal
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Anatoly Vershik, Pavel Zatitskiy, Fedor Petrov (2013)
Open Mathematics
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We study a wide class of metrics in a Lebesgue space, namely the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the ɛ-entropy of a measure space with an admissible metric, etc. These notions and related results are applied to the theory of transformations with invariant measure; namely, we study the asymptotic properties of orbits in the cone of admissible metrics with respect to a...
Karl Menger, Berthold Schweizer, Abe Sklar (1959)
Czechoslovak Mathematical Journal
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Nadezhda Ribarska (2000)
Studia Mathematica
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A characterization of topological spaces admitting a countable cover by sets of small local diameter close in spirit to known characterizations of fragmentability is obtained. It is proved that if X and Y are Hausdorff compacta such that C(X) has an equivalent p-Kadec norm and has a countable cover by sets of small local norm diameter, then has a countable cover by sets of small local norm diameter as well.
Karol Pąk (2008)
Formalized Mathematics
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This paper is a continuation of [12]. First some definitions needed to formulate Cantor's theorem on complete spaces and show several facts about them are introduced. Next section contains the proof of Cantor's theorem and some properties of complete spaces resulting from this theorem. Moreover, countable compact spaces and proofs of auxiliary facts about them is defined. I also show the important condition that every metric space is compact if and only if it is countably compact. Then...