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A note on the Ehrhard inequality

Rafał Latała (1996)

Studia Mathematica

We prove that for λ ∈ [0,1] and A, B two Borel sets in n with A convex, Φ - 1 ( γ n ( λ A + ( 1 - λ ) B ) ) λ Φ - 1 ( γ n ( A ) ) + ( 1 - λ ) Φ - 1 ( γ n ( B ) ) , where γ n is the canonical gaussian measure in n and Φ - 1 is the inverse of the gaussian distribution function.

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