A note on the Ehrhard inequality
Volume 118 / 1996
Studia Mathematica 118 (1996), 169-174
DOI: 10.4064/sm-118-2-169-174
Abstract
We prove that for λ ∈ [0,1] and A, B two Borel sets in with A convex, Φ^{-1}(γ_n(λA + (1-λ)B)) ≥ λΦ^{-1}(γ_n(A)) + (1-λ)Φ^{-1}(γ_n(B)), where γ_n is the canonical gaussian measure in ℝ^n and Φ^{-1} is the inverse of the gaussian distribution function.
