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Mutually Singular

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Definition
MeasureTheory

Two measures μ1,μ2\mu_{1},\mu_{2} on (X,M)(X,\mathscr{M}) are called mutually singular if and only if A1,A2M\exists A_{1},A_{2}\in\mathscr{M}, A1A2=A_{1}\cap A_{2}=\emptyset such that μi\mu_{i} is Concentrated on AiA_{i}, i=1,2i=1,2. We denote this using μ1μ2\mu_{1}\perp \mu_{2}

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