absolutely continuous measure

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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Now, we consider that [mu] is a probability measure on the compact set X, which is unnecessarily absolutely continuous measure with respect to Lebesgue measure [lambda].
Absolutely Continuous Measures with respect to Lebesgue Measures.
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.sub.N] (t)dt, where