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Dominated ergodic theorems in rearrangement invariant spaces. (English) Zbl 0913.46027

Summary: We study conditions under which dominated ergodic theorems hold in rearrangement invariant spaces. Consequences for Orlicz and Lorentz spaces are given. In particular, our results generalize the classical theorems for the spaces \(L_p\) and the classes \(L\log^nL\).

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47A35 Ergodic theory of linear operators
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