Lotz–Räbigerʹs nets of Markov operators in -spaces

The Lotz–Räbiger nets (LR-nets) introduced in Räbiger (1993) [18] under the name M-nets provide an appropriate setting for investigation various mean ergodic theorems in Banach spaces. In the present paper we prove several convergence theorems for LR-nets of Markov operators in L 1 -spaces which extend Theorems 1 and 5 from Emelʹyanov (2004) [8], and Theorem 1.1 from Lasota (1983) [11].