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In trying to prove the iterated formula for the Volterra operator, I get stuck with a basic integration problem. Let $x$ be any $L_2$ function. To what extent can we simplify, and in particular, swap the integral signs in the following expression: $$ \int_0^1 \left(\int_0^s x(u) \ du\right) \ ds $$ A change of variable would remove the $s$ from the second integral but that doesn't really help. I would appreciate any suggestion.

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