# Tag Archives: lebesgue measure

## A set that is not Lebesgue measurable

The Lebesgue measure $\lambda$ on the real line is a countably additive measure that assigns to each interval $[a,b]$ with $a \leq b$ its length $b-a$. Why construct the Lebesgue measure? It’s so that we can get around a blemish of the Riemann integral: namely, that the Riemann integration theory does not know how to […]

## The Sumset of Sets of Positive Measure

Today I shall continue in the spirit of my last post, which was essentially a revised set of notes on material for my qualifying exam. Here, and in the next post, we shall see two ways to prove that if $A$ and $B$ are Lebesgue-measurable subsets of the real line with positive measure, […]