Littlewood's Three Principles of Real Analysis - The Principles

The Principles

Littlewood stated the principles in his 1944 Lectures on the Theory of Functions as:

There are three principles, roughly expressible in the following terms: Every (measurable) set is nearly a finite sum of intervals; every function (of class Lλ) is nearly continuous; every convergent sequence of functions is nearly uniformly convergent.

The first principle is based on the fact that the inner measure and outer measure are equal for measurable sets, the second is based on Lusin's theorem, and the third is based on Egorov's theorem.

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