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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Slicing the cube in $ {\bf R}\sp{n}$ and probability (bounds for the measure of a central cube slice in $ {\bf R}\sp{n}$ by probability methods)


Author: Douglas Hensley
Journal: Proc. Amer. Math. Soc. 73 (1979), 95-100
MSC: Primary 60D05; Secondary 52A22
MathSciNet review: 512066
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Abstract: A cube of dimension n and side 1 is cut by a hyperplane of dimension $ n - 1$ through its center. The usual $ n - 1$ measure of the intersection is bounded between 1 and M, independent of n. The proof uses an inequality for sums of independent random variables.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0512066-8
PII: S 0002-9939(1979)0512066-8
Keywords: Thickness of a random variable, hyperplane slicing a cube
Article copyright: © Copyright 1979 American Mathematical Society