The first result in this direction was given by David Preiss in 1979: there exists a Gaussian measure γ on an (infinite-dimensional) separable Hilbert space H so that the Vitali covering theorem fails for (H, Borel(H), γ).
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In mathematics, the Vitali covering lemma is a combinatorial and geometric result commonly used in measure theory of Euclidean spaces.
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Finite version: Let be any finite collection of balls contained in d-dimensional Euclidean space Rd (or, more generally, in an arbitrary metric space).
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