Possible Duplicate:
Will moving differentiation from inside, to outside an integral, change the result?
In analysis there is such
theorem: Let $f:[0,1]\times\mathbb{R}\to\mathbb{R}$ $(x,\lambda)\mapsto f(x,\lambda)$ such continuous function of independent variable $x$ and real parameter $\lambda$ that all partial derivatives exist and continuous everywhere. And let $I(\lambda)=\int_{0}^{1}f(x,\lambda)dx$ Then $\frac{d}{d\lambda}I(\lambda)=\int_{0}^{1}\frac{\partial f(x,\lambda)}{\partial\lambda}dx.$
Is there some analogous statement for multiple integrals?
Thanks