Vector-valued ergodic theorems for multiparameter Additive processes II
Volume 97 / 2003
Colloquium Mathematicum 97 (2003), 117-129
MSC: Primary 47A35.
DOI: 10.4064/cm97-1-11
Abstract
Previously we obtained stochastic and pointwise ergodic theorems for a continuous $d$-parameter additive process $F$ in $L_{1}(({\mit\Omega},{\mit\Sigma},\mu);X)$, 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 $W(\cdot)= \mathop{\rm ess\,sup} \{ \|F(I)(\cdot)\| : I\subset [0, 1)^{d}\}$ is integrable on ${\mit\Omega}$.
