Abstract: With the probability inequality obtained in empirical processes and nature of the Euler weighting coefficients,the Euler summability of a sequence of random elements independent and identically distributed in empirical processes was investigated. The sufficient condition is obtained for the Euler strong law of large numbers in empirical processes. Under identical conditions, the Euler weak law of large numbers in empirical processes was spread to the situation of strong convergence.

Key words: empirical processes, weighted sums of random elements, bounded in probability, law of large numbers