We prove the following superexponential distribution inequality: for any integrable g on [0, 1)d with zero average, and any λ > 0, | { x∈ [ 0, 1 ) d : g≥λ } |≤ e − λ 2 /( 2 d ‖ S( g ) ‖ ∞ 2 ) , where ...

A direct proof is given for an inequality relating the expected absolute value of stopped Brownian motion to the expected time to stopping. This inequality was originally proved by means of the ...