simply decompose as and and observe that . The Dirac measure is a sigma-finite measure. Generalizations A discrete measure is similar to the Dirac measure, except that it is concentrated at countably many points instead of a single point. More formally, a measure on the real line is called a discrete measure (in respect to the Lebesgue measure) if its support is at most a countable set. See also Discrete measure Dirac delta function References Measures (measure theory)