Lotz–Räbiger's nets of Markov operators in L1-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 L1-spaces which extend Theorems 1 and 5 from Emel'yanov (2004) [8], , and Theorem 1.1 from Lasota (1983) [11].