A set of positive Gaussian measure with uniformly zero density everywhere.
David Preiss
University of Warwick, Coventry, UKElena Riss
Herzen State Pedagogical University of Russia, Saint Petersburg, RussiaJaroslav Tišer
Czech Technical University, Prague, Czechia
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Abstract
Existing negative results on invalidity of analogues of classical Density and Differentiation Theorems in infinite-dimensional spaces are considerably strengthened by a construction of a Gaussian measure in a separable Hilbert space for which the Density Theorem fails uniformly, i.e. there is a set of positive -measure such that
Cite this article
David Preiss, Elena Riss, Jaroslav Tišer, A set of positive Gaussian measure with uniformly zero density everywhere.. J. Eur. Math. Soc. 23 (2021), no. 7, pp. 2439–2466
DOI 10.4171/JEMS/1058