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Pointwise ergodic theorems for functions in Lorentz spaces $L_{pq}$ with p ≠ ∞

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Sato R.

Studia Mathematica

1994

tom 109

nr 2

209-216

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 ≠ ∞.

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1 Studia Mathematica

1 Sato R.

1 1994

Wyniki wyszukiwania

Pointwise ergodic theorems for functions in Lorentz spaces $L_{pq}$ with p ≠ ∞