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Vitali covering theorem in Hilbert space


Author: Jaroslav Tiser
Journal: Trans. Amer. Math. Soc. 355 (2003), 3277-3289
MSC (2000): Primary 28A50, 46G99
DOI: https://doi.org/10.1090/S0002-9947-03-03296-3
Published electronically: April 7, 2003
MathSciNet review: 1974687
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Abstract: It is shown that the statement of the Vitali Covering Theorem does not hold for a certain class of measures in a Hilbert space. This class contains all infinite-dimensional Gaussian measures.


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Additional Information

Jaroslav Tiser
Affiliation: Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27 Praha, Czech Republic
Email: tiser@math.feld.cvut.cz

DOI: https://doi.org/10.1090/S0002-9947-03-03296-3
Keywords: Vitali Covering Theorem, Gaussian measure, packing density
Received by editor(s): May 15, 2002
Received by editor(s) in revised form: January 24, 2003
Published electronically: April 7, 2003
Additional Notes: The author was supported by grants GA ČR 201/98/1153 and J04/98/210000010
Article copyright: © Copyright 2003 American Mathematical Society

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