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.

Read more about this topic:  Littlewood's Three Principles Of Real Analysis

Famous quotes containing the word principles:

    “The scope of modern government in what it can and ought to accomplish for its people has been widened far beyond the principles laid down by the old “laissez faire” school of political rights, and the widening has met popular approval.”
    —William Howard Taft (1857–1930)

    “[E]very thing is useful which contributes to fix us in the principles and practice of virtue.”
    —Thomas Jefferson (1743–1826)