Lecture 7 The Brunn - Minkowski Theorem and Influences of Boolean Variables Friday 25 , 2005 Lecturer : Nati Linial
نویسنده
چکیده
Theorem 7.1 (Brunn-Minkowski). If A, B ⊆ R n satisfy some mild assumptions (in particular, convexity suffices), then [vol (A + B)] 1 n ≥ [vol (A)] 1 n + [vol (B)] 1 n where A + B = { a + b : a ∈ A and b ∈ B}.
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Consider a vector space V (which can be of finite dimension). From linear algebra we know that at least in the finite-dimension case V has a basis. Moreover, there are more than one basis and in general different bases are the same. However, in some cases when the vector space has some additional structure, some basis might be preferable over others. To give a more concrete example consider the...
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Consider a vector space V (which can be of finite dimension). From linear algebra we know that at least in the finite-dimension case V has a basis. Moreover, there are more than one basis and in general different bases are the same. However, in some cases when the vector space has some additional structure, some basis might be preferable over others. To give a more concrete example consider the...
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