It appeared to me that his use of infinite definitely meant immeasurably large. That is there is no bound, and no repetition based on anything like going around the world and returning to your starting point. The repetitions he is referring to are those created by random chance in an immeasurably large space-time. After all if everything that we can observe is based on random happenings, then in an infinite space-time everything that can happen will happen an infinite number of times. On a smaller scale it is unlikely that a person will draw a royal flush in poker, but it does happen, and it happens many times. For us to exist the way we are is unlikely, but if you have an infinite space and time then we will happen again and again.
And of course as he explained we don't know if the universe is infinite or not.
Bill Gill
