Displaying similar documents to “On the range of analytic functions related to Caratheodory class”

Prevalence of "nowhere analyticity"

Françoise Bastin, Céline Esser, Samuel Nicolay (2012)

Studia Mathematica

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This note brings a complement to the study of genericity of functions which are nowhere analytic mainly in a measure-theoretic sense. We extend this study to Gevrey classes of functions.

The Relevance of Measure and Probability, and Definition of Completeness of Probability

Bo Zhang, Hiroshi Yamazaki, Yatsuka Nakamura (2006)

Formalized Mathematics

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In this article, we first discuss the relation between measure defined using extended real numbers and probability defined using real numbers. Further, we define completeness of probability, and its completion method, and also show that they coincide with those of measure.

Volume and multiplicities of real analytic sets

Guillaume Valette (2005)

Annales Polonici Mathematici

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We give criteria of finite determinacy for the volume and multiplicities. Given an analytic set described by {v = 0}, we prove that the log-analytic expansion of the volume of the intersection of the set and a "little ball" is determined by that of the set defined by the Taylor expansion of v up to a certain order if the mapping v has an isolated singularity at the origin. We also compare the cardinalities of finite fibers of projections restricted to such a set.

On capacitability and measurability

Maurice Sion (1963)

Annales de l'institut Fourier

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La relation entre la notion de mesurabilité du point de vue de la mesure extérieure de Carathéodory et celle de capacitabilité est étudiée, en particulier pour la capacité dans le potentiel classique. On introduit une notion de capacité abstraite, et dans des conditions très générales on montre que les ensembles analytiques sont capacitables dans ce sens. Plusieurs propriétés des ensembles analytiques sont déduites de cette étude.