A localization inequality for set functions |
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Authors: | László Lovász |
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Institution: | a Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA b Department of Mathematics-Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA |
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Abstract: | We prove the following theorem, which is an analog for discrete set functions of a geometric result of Lovász and Simonovits. Given two real-valued set functions f1,f2 defined on the subsets of a finite set S, satisfying for i∈{1,2}, there exists a positive multiplicative set function μ over S and two subsets A,B⊆S such that for i∈{1,2}μ(A)fi(A)+μ(B)fi(B)+μ(A∪B)fi(A∪B)+μ(A∩B)fi(A∩B)?0. The Ahlswede-Daykin four function theorem can be deduced easily from this. |
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Keywords: | Inequalities Set functions Four function theorem Discrete localization |
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