sigma algebras?

depending on how you wanna use mesures on the reals, it *seems* to me that something like having measures provide a sorta of "valuation" function on the elements of their sigma algebras might be useful? (or at least the generators of the sigma algebras etc etc, lets ignore filtrations )

eg, for the Real line (and approximations thereof), the sigma algebra generator set would be intervals (open or closed or clopen etc), because we can define the lesbegue/riemann measure on these to be the *length* ?

would this allow eg, talking about dirac delta as a measure/distribution?