absolutely continuous measure


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absolutely continuous measure

[ab·sə¦lüt·lē kən‚tin·yə·wəs ′mezh·ər]
(mathematics)
A sigma finite measure m on a sigma algebra is absolutely continuous with respect to another sigma finite measure n on the same sigma algebra if every element of the sigma algebra whose measure n is zero also has measure m equal to zero.
References in periodicals archive ?
Let us now consider the absolutely continuous measure [mu] on the unit circle given by d[mu](z) = [mu]'(z) [absolute value of dz] = [K.
Let us consider the absolutely continuous measures [mu] and [[mu].