Given $f$ a function measurable in $[0,\infty]$ defined as $$\frac{d\mu}{d\nu}$$

such that, for every measurable set $A$ we have:

$$\mu(A)=\int_A{}fd\nu$$ the function $f$ is called $Radon - Nikodym\ derivative$ of $\mu$ respect to $\nu$

My question is: is it possible to define a $fractional\ Radon - Nikodym\ derivative$ of $\mu$ respect to $\nu$?

Thanks.