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Two measures μ1,μ2\mu_{1},\mu_{2}μ1,μ2 on (X,M)(X,\mathscr{M})(X,M) are called mutually singular if and only if ∃A1,A2∈M\exists A_{1},A_{2}\in\mathscr{M}∃A1,A2∈M, A1∩A2=∅A_{1}\cap A_{2}=\emptysetA1∩A2=∅ such that μi\mu_{i}μi is Concentrated on AiA_{i}Ai, i=1,2i=1,2i=1,2. We denote this using μ1⊥μ2\mu_{1}\perp \mu_{2}μ1⊥μ2
A Summary of MATH 891
Radon-Nikodym Theorem