Abstract: | For Brownian motion B denote by Bδ its polygonal approximation corresponding to a partition δ of [0,1]. It is proved that if E(f1|Xt|p dt<∞ for some p>2 then converges to in mean as the mesh |Δ|→0 provided the symmetric (Stratonovich) stochastic integral is determined (in the sense given in [4]) |