Riemann Zeta Function as a Multiple Integral

Theorem
For $n \in \N \setminus \{ 1 \}$, the Riemann zeta function is given by:


 * $\displaystyle \zeta \left({n}\right) = \int_{\left[{0, 1}\right]^n} \frac 1 {1 - \prod_{i \mathop = 1}^n x_i} \prod_{i \mathop = 1}^n \mathrm d x_i$

Where $[0,1]^n$ denotes the Cartesian $n$th power of $[0,1]$.