Pro-Chern-Schwartz-MacPherson class for DM stacks

We generalize the definition of Pro-Chern-Schwartz-MacPherson (Pro-CSM) class of Aluffi for schemes to not necessarily proper DM stacks. The Pro-CSM class of constructible functions on a DM stack $\text{cX}$ can be similarly defined. In the case that $\text{cX}$ is proper, the Pro-CSM class of the Behrend function of $\text{cX}$ is the same as the Chern-Schwartz-MacPherson (CSM) class for the Behrend function. The integration of this class over $\text{cX}$ gives rise to the weighted Euler characteristic corresponding to the Behrend function, thus proving a conjecture of Behrend.