Masoud Ajami - Department of Statistics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
Vahid Fakoor - Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran.

In this paper, by using a sampling procedure, subjected to length-bias, the cumulative distribution function F(.) is estimated by the kernel-type estimator. Also.under suitable conditions, the extended Glivenko-Cantelli theorem for that estimator is proved

Extended Glivenko-Cantelli theorem, Length-biased data, Smoothed estimator, Strong consistency