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This paper deals with the existence, the uniqueness and an approximation scheme of the solution to sweeping processes perturbed by a continuous signal of finite $p$-variation with $p\in [1,3[$. It covers pathwise stochastic noises directed by a fractional Brownian motion of Hurst parameter greater than $1/3$., Comment: 27 pages

We present several versions of Olech's lemma and Visintin's theorem inPettis integration and L~t[E] in the same vein as Amrani-Castaing-Valadier [4] andBenabdellah-Castaing [12] ., Convex Analysis and Chaos : The Third Symposium on Nonlinear Analysis, July 23-25, 1998 Josai University, edited by Kiyoko Nishizawa

New characterizations of conditionally weakly compact (resp. relatively weakly compact) subsets in Banach space $E$ and $L^1_E(\mu)$ are presented. We discuss also several types of convergence in $L^1_E(\mu)$, in particular we generalize Szlenk's theorem on Cesàro norm-convergence of weakly null sequences in $L^1_\mathbb{R}(\mu)$ to the norm-summability with respect to a class of regular method of summability of weakly null sequences in $L^1_H(\mu)$ where $H$ is a Hilbert space.