One of the reasons subharmonic functions are interesting is that if you take their laplacian, you get a measure (and conversely any finite Radon measure with compact support can be obtained in this way).
Observation : if you take the laplacian of the difference between two subharmonic functions, you should get a signed measure. For example, I know that any smooth function is the difference of two smooth subharmonic functions. Taking the laplacian, you get a signed measure with density with respect to Lebesgues.
Question : is there a bit of theory available in this direction (e.g. are differences of 2 subharmonic functions interesting as functions), that would be similar to the classical theory of subharmonic functions and Radon measures ? Or is there nothing to be said that doesn't just follow from the usual theory ?