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Mutually Singular

Let $M$ be a Sigma Algebra $M$, and let $\lambda_1$ and $\lambda_2$ be Measures on $M$. If there Exists a pair of disjoint Sets $A$ and $B$ such that $\lambda_1$ is Concentrated on $A$ and $\lambda_2$ is Concentrated on $B$, then $\lambda_1$ and $\lambda_2$ are said to be mutually singular, written $\lambda_1\perp\lambda_2$.

See also Absolutely Continuous, Concentrated, Sigma Algebra


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

© 1996-9 Eric W. Weisstein