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Nov 4, 2011 at 21:57 comment added Will Sawin Arguably, that should be the answer to the question.
Nov 4, 2011 at 20:39 comment added Michael Greinecker The result of taking the quotient of a sigma-algebra by the ideal of null sets is known as a measure algebra. And it is a rather rich structure. Fremlin devotes more than 600 pages (the entire 3rd volume) on measure algebras in his encyclopedic series on measure theory. How much structure remains is conclusively answered by Maharam's classification theorem: ncbi.nlm.nih.gov/pmc/articles/PMC1078424 (Theorems 1 and 2)
Nov 4, 2011 at 18:18 history answered Will Sawin CC BY-SA 3.0