This article is cited in 5 papers

Ergodic theorems for contractions in Orlicz–Kantorovich lattices

B. S. Zakirov^a, V. I. Chilin<sup>b

a</sup> Tashkent Institute of Railway Transport Engineers, Tashkent, Uzbekistan
^b National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: We obtain some versions of ergodic theorems for positive contractions in the Orlicz–Kantorovich lattices $L_M(m)$ associated with a measure $m$ taking values in the algebra of measurable real functions. The proof is carried out by representing $L_M(m)$ as measurable bundles of classical Orlicz function spaces.

Keywords: Orlicz–Kantorovich lattice, measurable Banach bundle, positive contraction, ergodic theorem.

UDC: 517.98

Received: 11.03.2008

 English version: Siberian Mathematical Journal, 2009, 50:6, 1027–1037

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