The measure of a translated ball in uniformly convex spaces |
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Authors: | Micha? Ryznar Tomasz ?ak |
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Institution: | (1) Institute of Mathematics, Technical University, Wybrzee Wyspiaskiego 27, 50-370 Wrocaw, Poland |
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Abstract: | Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r
q
, whereq depends on the properties of the norm. We specify it in the case ofL
spaces, >1. |
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Keywords: | Gaussian measures stable measures density of a norm uniformly convex spaces |
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