Let be a positive measure on a sigma-algebra , and let be an arbitrary (real or complex) measure on . If there is a set such that for every , then is said to be concentrated on . This is equivalent to requiring that whenever .
Concentrated
See also
Absolutely Continuous, Mutually SingularExplore with Wolfram|Alpha
References
Rudin, W. Functional Analysis, 2nd ed. New York: McGraw-Hill, p. 121, 1991.Referenced on Wolfram|Alpha
ConcentratedCite this as:
Weisstein, Eric W. "Concentrated." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Concentrated.html