This paper studies the convergence rate of randomized quasi-Monte Carlo (RQMC) for discontinuous functions, which are often of infinite variation in the sense of Hardy and Krause.

Viet Ngo, A Structure Theorem for Discontinuous Derivations of Banach Algebras of Differential Functions, Proceedings of the American Mathematical Society, Vol. 102, No. 3 (Mar., 1988), pp. 507-513 ...