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 independent and dependent random variables. It extends results from the literature by making use of the cover number properties of stochastically Lipschitz-continuous averages on the one hand and convergence speeds of averages of bounded functions on the other hand. The resulting conditions for uniform laws of large number for stochastically Lipschitz-continuous averages of functions trade off heterogeneity and dependence against trending in the Lipschitz function of the function class involved.