Show the Lebesgue-measure of the image of the Cantor-Function is equal to 1?

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Currently strugging to proof the following:

Let f be the Cantor-Function defined as the limit of affine functions (so not the definition with base 3), C the cantor set and $\lambda$ the Lebesgue measure on $\mathbb{R}$.

Show that $$\lambda (f(C)) = 1$$

I have already proven that C is negligible but I don't really know how that helps me in this case.