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.
References in periodicals archive ?
Contract notice: Contract for the award of service management, operation, maintenance and technical assistance of avl systems (visual aids bright) and its system of remote control and monitoring of electrical substations of power associated with them, generating sets and systems of absolute continuity, the electrical substations in service of radio services and ground surveys of papi systems , the photometric measurements of runway lights and beacon towers airside society airport valerio catullo di verona villafranca spa located at the airport valerio catullo di verona villafranca and at the gabriele d~annunzio airport brescia montichiari, both operating in cat iiib .
Contract for the assignment 24 h, seven days a week, service management, operation, maintenance and technical assistance of AVL systems (Visual Aids Bright) and its system of remote control and monitoring of electrical substations of power associated with them, generating sets and systems of absolute continuity, the electrical substations in service of radio and is also inclusive of the services of ground surveys PAPI systems, the photometric measurements of all the lights AVL system that is elevated and recessed lighting towers airside society Airport Valerio Catullo di Verona Villafranca SpA and located at the Airport Valerio Catullo di Verona Villafranca Airport and at the Gabriel D~Annunzio in Brescia Montichiari.
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.
THETA]]] admits a classical function as density, so that the need of introducing a concept of absolute continuity for random closed sets arises in a natural way.
In order to respond to this further requirement, we propose a concept of absolute continuity for random closed sets.
A definition of absolute continuity requires a reference measure; for a random point in [R.
A random point is a particular random closed set of Hausdorff dimension 0; we now introduce a definition of absolute continuity for random closed sets, such that analogous relations for random sets hold with any Hausdorff dimension n [member of] {0, 1, .
Remark 10 In the particular case that [THETA] = X is a random variable, Definition 9 coincides with the usual definition of absolute continuity of a random variable.
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.
They range between 100% for an automatic interruption to 0% for an absolute continuity.
Our focus will be to ensure absolute continuity of care, thus securing confidence from every stakeholder during this phasing in period.