ABSTRACT
In his 1944 book, Lectures on the Theory of Functions (Oxford), J. E. Littlewood (1885-1977) set out three principles of real analysis which have come to be known by this chapter’s title. The statement of these principles is quoted on p. 71 of Royden (1971), and can be summarized as follows:
Every Lebesgue measurable set of finite measure is “nearly” the finite union of open intervals.
Every Lebesgue measurable function is “nearly” continuous.
Every convergent sequence of Lebesgue measurable functions is “nearly” uniformly convergent.
