User:TakuyaMurata/Local study of functions

Theorem (Euler's relation): ''Every $$f \in C^\infty(\mathbf{R}^n / \{0\})$$ is homogeneous of order $$m$$ if and only if:
 * $$\left(\sum_j x_j{\partial \over \partial x_j} - m\right) f = 0.$$''