Standard probability space

Summary

A standard probability space is a probability space that looks like a simple model after null sets are removed. The model is an interval with Lebesgue measure, a countable set of atoms, or a combination of both. The theory goes back to von Neumann in 1932 and was shaped by Rokhlin, who called these spaces Lebesgue spaces. Most probability spaces of analysis are standard, and on standard spaces conditional probabilities and disintegrations behave well. For this reason ergodic theory and probability often assume their spaces to be standard.