When one talks about electrical **charge distribution**, one usually refers to the way in which charge is "spread" through space. For example one might say that charge is distributed continuously with a 
- volume charge density $\rho~(C/m^3)$  in a volume,
- surface charge density $\sigma~(C/m^2)$  on a surface,
- linear charge density $\lambda~(C/m)$  on a curve.

Alternatively we could have a discrete charge distribution in which the total charge $q$ in a region of space is located at various points. 

However, in mathematics there is also the concept of **distributions** which is a sort of a [generalization of a function][1]. Formally a distribution is a functional that acts on test functions. A famous example of this is the delta Dirac function $\delta$ which, in the case of a test function $\varphi$ is defined as $\delta(\varphi) = \varphi(0) $.

My question is: is there a connection between the concepts of "charge distribution" and "mathematical distribution (as described earlier)"? If so, what are the distributions and the test functions in the previous cases (where we have $\rho$, $\sigma$ and $\lambda$)?



  [1]: https://en.wikipedia.org/wiki/Distribution_(mathematics)