Let $f$ is continuous function on $B =I_1 \times I_2 \times\cdots\times I_n$ where the $I_i$ are closed intervals in $\mathbb R$ and $σ \colon \{1,2,...,n\}\to\{1,2,...,n\}$ is a one-to-one permutation.
Show that $$ \int_B f(x)\, dx = \int_{I_{σ(n)}} \int_{I_{σ(n-1)}} \cdots \int_{I_{σ(1)}} f(x)\,dx_{σ(1)} \ldots dx_{σ(n)}.$$
I don't know if this is an extension of Fubini-Tonelli's theorem, but it looks similar.
If I understood a proof of Fubini-Tonelli's theorem, would I easily understand this problem?