I'm trying to prove the integral of the cantor function on [0,1] is equal to 1/2.
I'm thinking of using a symmetry argument by using the fact that the function is 1/2 on [1/3,2/3]. Then arguing that for every region where the function is less than 1/2, there is an equal size region where the function is above 1/2 by the same amount.
But I'm not sure how to formalise this argument using mathematics as there are an infinite number of intervals.
Is this the correct approach to use? I haven't covered topics in measure theory yet so am fully sure how to use those sorts of concepts.