## 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 […]