singular measure

See singular measure for examples of measures that are not absolutely continuous.

For example, the Dirac delta function is a singular measure.

Simulations of systemic networks can help to decide the long-term effects of singular measures.

Intuitive formal originality as a singular measure of merit risks ignoring the essential public role unique to this artistic discipline.

Then this gives a singular measure on [0, 1] singular to Lebesgue measure.

Via Lebesgue's decomposition theorem, every measure can be decomposed into the sum of an absolutely continuous measure and a singular measure.

A refined form of Lebesgue's decomposition theorem decomposes a singular measure into a singular continuous measure and a discrete measure.

Those tempted to think that the university, in importing the chapel, has added a singular measure of cultural depth to eastern Kansas should note that this region does not lack for history.

Furthermore, one can show that the usual Lebesgue measure on the interval is an image of the Haar measure on the Cantor set, while the natural injection into the ternary set is a canonical example of a singular measure.