The notion of an L1–norm density estimator process indexed by a class of kernels is introduced. Then a functional central limit theorem and a Glivenko–Cantelli theorem are established for this process. While assembling the necessary machinery to prove these results, a body of Poissonization techniques and restricted chaining methods is developed, which is useful for studying weak convergence of...

In the paper we define the convergence of compact fuzzy sets as a convergence of α-cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy variables and show relations with convergence of their fuzzy distributions. In this context we prove a general formulation of the Strong Law of Large Numbers for fuzzy sets and fuzzy variables with Archi...