# absolutely continuous function

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## absolutely continuous function

[¦ab·sə‚lüt·lē kən¦tin·yə·wəs ′fəŋk·shən]
(mathematics)
A function defined on a closed interval with the property that for any positive number ε there is another positive number η such that, for any finite set of nonoverlapping intervals, (a1, b1), (a2, b2), … , (an, bn), whose lengths have a sum less than η, the sum over the intervals of the absolute values of the differences in the values of the function at the ends of the intervals is less than ε.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Then they discuss induction, isoenergetic sets: generalized eigenfunctions of the Schrodinger operator, and proof of absolute continuity of the spectrum.
With the acquisition of Insight's Komori division, Komori India will continue to retain all the employees of Insight in its new team and this will help in ensuring absolute continuity with the existing sales and service activities.
Taking into account absolute continuity of the integrals of the functions a and [a.sub.1] and letting [epsilon] [right arrow] 0, we get
Thanks to the weak convergence of [u.sub.n] in [H.sup.1.sub.0]([OMEGA]) and the absolute continuity of the integral, there exists [k.aub.0] independent from n such that, for k > [k.sub.0], we have
The visually simultaneous events, contrary in their implied duration, confound our sense of temporality and, perhaps inadvertently, deny the "absolute continuity" that Straub deplored as a falsity of bourgeois cinema.
argues that the council must be seen from a historical perspective; "de-historicizing" it by submitting it to the ideology of "absolute continuity" can only lead to a re-Europeanization of a now global Catholicism (10).
A concept of absolute continuity of random closed sets arises in a natural way in terms of the absolute continuity of suitable mean content measures, with respect to the usual Lebesgue measure on [R.sup.d].
"He was there at the beginning and end of every tour providing absolute continuity of treatment."
of Barcelona) covers the integration by parts and absolute continuity of probability laws, finite dimensional Malliavin calculus, representations of Weiner functions, the criteria for absolute continuity and smoothness of probability laws, stochastic partial differential equations driven by spatially homogeneous Gaussian noise, Malliavin regularity of solutions of stochastic backward differential equations (SPDEs) and analysis of the Malliavin matrix of solutions of SPDEs.
Conti's central assumption is that, despite a change in emphasis, there was absolute continuity in Farrer's theological method: he sought to demonstrate the conceivability of theism by uncovering the metaphysical presuppositions of being.
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