Let X be a multivariate random variable and (X_n)_N a sequence of realisations of X which are not necessarily assumed to be independent. We derive a generalization of GLIVENKO-CANTELLI theorem under a φ-mixing,condition on the sequence (X_n). This result together with an improvement of the uniform rate of convergence on a compact set of density kernel estimate leads to uniform rate of convergence of hazard kernel estimate. This last result is illustrated by means of Monte Carlo experiments