Littlewood's three principles

Summary

Littlewood's three principles are rules of thumb for working with Lebesgue measure on the real line. Every measurable set is nearly a finite union of intervals, and every measurable function is nearly continuous. Every convergent sequence of measurable functions is nearly uniformly convergent. Each principle has a precise form, and the last two are Lusin's theorem and Egorov's theorem. They let one transfer arguments for simple objects to general measurable ones.