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Note on the Ahlswede-Daykin inequality

✍ Scribed by Klaus Reuter

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
178 KB
Volume
65
Category
Article
ISSN
0012-365X

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✦ Synopsis

Given a finite boolean lattice L and four functions tr, fl, y, 6 of L to the nonnegative reals with oc(x)fl(y) <~ y(x v y)6(x A y) for all x, y e L. We show that

Here x' denotes the complement of x and X v X' stands for {Xl v x~ I xl, x2 e X). This inequality turns out to be equivalent in a certain sense to the Ahlswede-Daykin inequality. We also apply our basic ideas to a special case of a conjecture of Fiirstenberg.

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