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The Gaussian Isoperimetric Inequality and Transportation

✍ Scribed by Gordon Blower

Book ID
111558952
Publisher
Springer
Year
2003
Tongue
English
Weight
164 KB
Volume
7
Category
Article
ISSN
1385-1292

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Let g be a smooth function on R n with values in [0, 1]. Using the isoperimetric property of the Gaussian measure, it is proved that ,(8 &1 (Eg))&E,(8 &1 ( g)) E |{g|. Conversely, this inequality implies the isoperimetric property of the Gaussian measure.