Lusin's Theorem

The theorem proves that every measurable function coincides with a continuous function on a set of large measure.

[bapaden]

This is a beautiful theorem. I find the intuition to be that a topological space is "almost" a sigma algebra and since the definition of a continuous function (inverse image of open set is open) very similar to the definition of a measurable function (inverse image of measurable set is measurable) we might expect that a measurable function is "almost" continuous. The proof easier to understand with this picture in mind.

[happyman]

hi what software are you using to produce this? it looks really neat. :)