Let be a sigma-algebra , and let and be measures on . If there exists a pair of disjoint sets and such that is concentrated on and is concentrated on , then and are said to be mutually singular, written .
See alsoAbsolutely Continuous, Concentrated, Sigma-Algebra
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ReferencesRudin, W. Functional Analysis, 2nd ed. New York: McGraw-Hill, p. 121, 1991.
Referenced on Wolfram|AlphaMutually Singular
Cite this as:
Weisstein, Eric W. "Mutually Singular." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MutuallySingular.html