For those who didn't make it to page 249 of "The Anthropic Cosmological Principle" by John Barrow and Frank Tipler, I quote:
"In a randomly infinite Universe, any event occurring here and now with finite probability must be occurring simultaneously at an infinite number of other sites in the Universe. It is hard to evaluate this idea any further, but one thing is certain: if it is true then it is certainly not original!"
By the way it is a great book. If you don't like equations just skip those bits: you don't have to grok the equations to get a lot out of it.