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Absolutely Continuous

Let $\mu$ be a Positive Measure on a Sigma Algebra $M$ and let $\lambda$ be an arbitrary (real or complex) Measure on $M$. Then $\lambda$ is absolutely continuous with respect to $\mu$, written $\lambda\ll\mu$, if $\lambda(E)=0$ for every $E\in M$ for which $\mu(E)=0$.

See also Concentrated, Mutually Singular


Rudin, W. Functional Analysis, 2nd ed. New York: McGraw-Hill, pp. 121-125, 1991.

© 1996-9 Eric W. Weisstein