In any one region of space, all you need is a finite dimensional Hilbert space to describe what's going on. Are there an infinite number of regions of space? Something we don't actually know. Nicholas Vocrott says accepting that some universes are those in which very rare things happen does not mean they will continue to happen. The probability that a bunch of very unlikely things happen in the Everady and multiverse is just really, really tiny,. Just like it is in quantum mechanics.