EN
Previously we obtained stochastic and pointwise ergodic theorems for a continuous d-parameter additive process F in L₁((Ω,Σ,μ);X), where X is a reflexive Banach space, under the condition that F is bounded. In this paper we improve the previous results by considering the weaker condition that the function $W(·) = ess sup{||F(I)(·)||: I ⊂ [0, 1)^{d}}$ is integrable on Ω.