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We prove a local version of the Khintchine inequality for the spaces Exp L p ([0, 1]) of functions having p-th exponential integrability, for 1 ≤ p ≤ 2. The result also holds for the lacunary Walsh series.doi:10.1090/s0002-9939-2011-10890-6 fatcat:tf3qjhhxlffuboi47ndj2coveu