A Mass Transport Proof of the Ergodic Theorem

Abstract

It is known that a gambler repeating a game with positive expected value has a positive probability to never go broke. We use the mass transport method to prove the generalization of this fact where the gains from the bets form a stationary, rather than an i.i.d., sequence. Birkhoff's ergodic theorem follows from this by a standard argument.

4 pages, 2 figures