Does anyone know if the notion of a Dirac measure was named after P.A.M. Dirac? If yes, did he actually introduce it, or is it because integration w.r.t. a Dirac measure does what the so-called Dirac delta function is supposed to be used for?
Yes, the Dirac measure is so named because it performs the same action as Dirac's "delta function." I don't believe Dirac used the measure theory formalism, however - he was a physicist.