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Let $\mu$ be a Positive Measure on a Sigma Algebra $M$, and let $\lambda$ be an arbitrary (real or complex) Measure on $M$. If there is a Set $A\in M$ such that $\lambda(E)=\lambda(A\cap E)$ for every $E\in M$, then $\lambda$ is said to be concentrated on $A$. This is equivalent to requiring that $\lambda(E)=0$ whenever $E\cap A=\emptyset$.

See also Absolutely Continuous, Mutually Singular


Rudin, W. Functional Analysis, 2nd ed. New York: McGraw-Hill, p. 121, 1991.

© 1996-9 Eric W. Weisstein