• Corpus ID: 211132596

Vector valued unified martingale and ergodic theorems with continuous parameter

  title={Vector valued unified martingale and ergodic theorems with continuous parameter},
  author={Farruh Shahidi},
  journal={arXiv: Dynamical Systems},
  • F. Shahidi
  • Published 15 February 2020
  • Mathematics
  • arXiv: Dynamical Systems
We prove martingale-ergodic and ergodic-martingale theorems with continuous parameter for vector valued Bochner integrable functions. We first prove almost everywhere convergence of vector valued martingales with continuous parameter. The norm as well as almost everywhere convergence of martingale-ergodic and ergodic-martingale averages are given. We also obtain the dominant and maximal inequalities. Finally, we show that a.e. martingale-ergodic and ergodic-martingale theorems will coincide… 



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