# Vitali’s Theorem

There exists a set $V\subset[0,1]$ which is not Lebesgue measurable. Notice that this result requires the Axiom of Choice.

Title Vitali’s Theorem VitalisTheorem 2013-03-22 13:45:47 2013-03-22 13:45:47 paolini (1187) paolini (1187) 5 paolini (1187) Theorem msc 28Axx existence of non measurable sets Integral2 LebesgueMeasure PsuedoparadoxInMeasureTheory ExampleOfFunctionNotLebesgueMeasurableWithMeasurableLevelSets