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 $[0,1[$

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

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