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Dec 14, 2017 at 21:37 comment added Kusma And no, it doesn't work, as this is just the same as the $L^1$ norm on step functions so the closure is all of $L^1$. The sets you get from Egorov's theorem aren't good enough to create step functions.
Dec 14, 2017 at 16:06 history undeleted Kusma
Dec 14, 2017 at 16:06 history deleted Kusma via Vote
Dec 14, 2017 at 16:03 comment added Kusma sorry, I meant this to be a "comment", not an answer...
Dec 14, 2017 at 16:00 history answered Kusma CC BY-SA 3.0