Braverman, Michael; Rubshtein, Ben-Zion; Veksler, Alexander Dominated ergodic theorems in rearrangement invariant spaces. (English) Zbl 0913.46027 Stud. Math. 128, No. 2, 145-157 (1998). 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 \(L\log^nL\). Cited in 2 Documents 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 Keywords:Hardy-Littlewood property; dominated ergodic theorems; rearrangement invariant spaces; Orlicz and Lorentz spaces PDFBibTeX XMLCite \textit{M. Braverman} et al., Stud. Math. 128, No. 2, 145--157 (1998; Zbl 0913.46027) Full Text: EuDML