I've done some googling, but there are a few different notations employed, and I don't feel I've found an answer I'm comfortable with.
Suppose you have a sample of 'i.i.d' observations $X_1,\dots,X_n\sim f$, and want to take an expectation of some function $g$ which is built on the order statistics of the sample. The first step requires acknowledgement of the joint p.d.f these observations, but what becomes the boundary of integration for this multiple dimensional integral? My best guess is setting up the intervals : $$\int_{-\infty}^\infty\int_{-\infty}^{x_{n}}\int_{-\infty}^{x_{n-1}}\dots\int_{-\infty}^{x_{2}}\ \left[g\cdot\prod_{k=1}^nf(x_k)\right]\ {dx}_1{dx}_2\dots{dx}_n$$ but it's not immediately clear that this is correct.
The lack of attention on the question makes me think that there may be something in the problem statement which may be ambiguous or better described. Any feed back (even if you don't know an answer) on the formulation of the problem would be greatly appreciated.