UNIFORM LAWS OF LARGE NUMBERS AND STOCHASTIC LIPSCHITZ-CONTINUITY

This paper presents weak and strong uniform laws of large numbers for stochastically Lipschitz-continuous averages of functions of independe nt and dependent random variables. It extends results from the literat ure by making use of the cover number properties of stochastically Lip schitz-continuous averages on the one hand and convergence speeds of a verages of bounded functions on the other hand. The resulting conditio ns for uniform laws of large number for stochastically Lipschitz-conti nuous averages of functions trade off heterogeneity and dependence aga inst trending in the Lipschitz function of the function class involved . (C) 1998 Elsevier Science S.A. All rights reserved.