Displaying similar documents to “Prevalence of 'nowhere analyticity'”

Stable families of analytic sets

Pandelis Dodos (2003)

Colloquium Mathematicae

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We give a different proof of the well-known fact that any uncountable family of analytic subsets of a Polish space with the point-finite intersection property must contain a subfamily whose union is not analytic. Our approach is based on the Kunen-Martin theorem.

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.