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_|_lambda_2.

See also

Absolutely Continuous, Concentrated, Sigma-Algebra

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

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Mutually Singular

Cite this as:

Weisstein, Eric W. "Mutually Singular." From MathWorld--A Wolfram Web Resource.

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