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Information inequalities and concentration of measure. (English) Zbl 0880.60018

Summary: We derive inequalities of the form \(\Delta(P,Q)\leq H(P|R)+ H(Q|R)\) which hold for every choice of probability measures \(P\), \(Q\), \(R\), where \(H(P|R)\) denotes the relative entropy of \(P\) with respect to \(R\) and \(\Delta(P,Q)\) stands for a coupling type “distance” between \(P\) and \(Q\). Using the chain rule for relative entropies and then specializing to \(Q\) with a given support we recover some of Talagrand’s concentration of measure inequalities for product spaces.

MSC:

60E15 Inequalities; stochastic orderings
28A35 Measures and integrals in product spaces
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