A measure concentrated on a set which is at most countable. More generally, let and be measures (usually with alternating signs) defined on a semi-ring of sets (with its -ring of measurable sets). The measure is said to be a discrete measure with respect to the measure if is concentrated on a set of -measure zero which is at most countable and any one-point subset of which is -measurable. For instance, the discrete Lebesgue–Stieltjes measure of linear sets is equal on half-intervals to the increment of some jump function, which is of bounded variation if is bounded, and which is non-decreasing if is non-negative.
|||A.N. Kolmogorov, S.V. Fomin, "Elements of the theory of functions and functional analysis" , 1–2 , Graylock (1957–1961) (Translated from Russian)|
Discrete measure. A.P. Terekhin (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Discrete_measure&oldid=12919