On Uniform Laws of Large Numbers for Smoothed Empirical Measures
We consider function-indexed smoothed empirical measures on linear metric spaces and focus on uniform laws of large numbers (ULLN) comparable with Glivenko-Cantelli results in the non-smoothed case. Using the random measure process approach we are able to give a set of sufficient conditions for a ULLN which are different from the ones known in the literature and are more close to being necessary.
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