The simplest example of a discrete measure on the real line is the Dirac delta function
Measure for Measure | Ecclesiastical Jurisdiction Measure 1963 | Gaussian measure | Discrete cosine transform | discrete cosine transform | Projection-valued measure | Measure B | Locally finite measure | Lebesgue measure | grain (measure) | Discrete Hartley transform | Dirac measure | Borel measure | A Measure of Salvation |