# What are the lebesgue - measurables sets of $[0,1[$

I am trying to prove that a function defined on $$[0,1[$$ is lebesgue - measurable, but I am not sure about the lebesgue - measurables sets on $$[0,1[$$

• What is your definition of "Lebesgue measurable subset of $E$", where $E$ is some given subset of ${\mathbb R}?$ – Dave L. Renfro Nov 10 '18 at 15:17
• The basis for the Lebesgue $\sigma$-algebra are sets of the form $[a,b],[a,b),(a,b],(a,b)$ for $0\leq a,b\leq 1$. – Yanko Nov 10 '18 at 15:18