Pointwise ergodic theorems for functions in Lorentz spaces $L_{pq}$ with p ≠ ∞
Volume 109 / 1994
Studia Mathematica 109 (1994), 209-216
DOI: 10.4064/sm-109-2-209-216
Abstract
Let τ be a null preserving point transformation on a finite measure space. Assuming τ is invertible, P. Ortega Salvador has recently obtained sufficient conditions for the almost everywhere convergence of the ergodic averages in $L_{pq}$ with 1 < p < ∞, 1 < q < ∞. In this paper we obtain necessary and sufficient conditions for the almost everywhere convergence, without assuming that τ is invertible and only assuming that p ≠ ∞.
