60E15, 62N05, 90B25, 94A17, 94A24.

Ebrahim and Pellery [7] and Ebrahim [4] proposed the Shannon residual entropy function as a dynamic measure of uncertainty. In this paper we introduce and study a generalized information measure for residual lifetime distributions. It is shown that the proposed measure uniquely determines the distribution function. Also, characterization results for some lifetime distributions are discussed. Some discrete distribution results are also addressed.;