Shapiro, Alexander and Xu, Huifu
Uniform laws of large numbers for set-valued mappings
and subdifferentials of random functions
Journal of Mathematical Analysis and Applications, 325, . (doi:10.1016/j.jmaa.2006.02.078).
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We derive a uniform (strong) Law of Large Numbers (LLN) for random set-valued mappings. The result can be viewed as an extension of both, a uniform LLN for random functions and LLN for random sets. We apply the established results to a consistency analysis of stationary points of sample average approximations of nonsmooth stochastic programs.
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