Consider the following transformation of the integration measure $dX d\psi_1 d\psi_2$: where $\psi_1$ $\psi_2$,$\varepsilon^1$, and $\varepsilon^2$ are Grassman variables.
$\delta_\varepsilon X= \varepsilon^1 \psi_1+ \varepsilon^2 \psi_2$
$\delta\psi_1= \varepsilon^2 \partial h$
$\delta\psi_2= -\varepsilon^1 \partial h$. The problem asked to show that the above integration measure is invariant under this transformation. My approach to the first one was to just use the fact that $\int \psi_1 \dots \psi_n d \psi_1 \dots d\psi_n=1$, and relate it to the bosonic "standard" variables which return $\int dX= \int 1 dX=X$. However, for the other two, I know that since $\int \psi d \psi=1$, it should follow easily. But what does the $h$ denote in the differential? and is this argument headed in the right direction?
Many thanks to all of you.