Lebesgue measure


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Lebesgue measure

[lə′beg ‚mezh·ər]
(mathematics)
A measure defined on subsets of euclidean space which expresses how one may approximate a set by coverings consisting of intervals.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Here meas A denotes the Lebesgue measure of a measurable set A C R.
Let [DELTA] denote the unit disc in C and dA the normalized Lebesgue measure on [DELTA].
Hypervolume (HV) [40] is also known as the S measure or the Lebesgue measure [41, 42].
([A.sub.2]) The measure [mu] is absolutely continuous with respect to [lambda], where [lambda] is the Lebesgue measure.
We assume that the random vector [omega] has a distribution function with respect to the Lebesgue measure denoted by f.
where d[sigma] denotes normalized Lebesgue measure on T.
Let [lambda] be the one dimensional Lebesgue measure. For each x [member of] X \ {0}, set
Therefore, the removing of a "small set" (in Lebesgue measure sense) is needed; that is, we require [omega] [member of] [O.sub.[gamma],[tau]].
of inconsistency Continuum PC matrices gauge theories Consistency 0-curvature Consistency in [OMGA](X, Y) = 0 3 x 3 matrices with X, Y tangent to [[DELTA].sub.2] Koczkodaj's [sup.sub.M] inconsistency [parallel][OMEGA][parallel] indicator ii Minimization Minimization of the of inconsistency curvature norm Table 2 Continuum Discretized integration integration PC matrices Heuristic Lebesgue measure ?
Let T := [-[pi], [pi]].A measurable 2[pi]-periodic function [omega] : T [right arrow] [0, [infinity]] is called a weight function if the set [[omega].sup.-1] ({0, [infinity]}) has the Lebesgue measure zero.
In addition, from de Figueiredo-Gossez [4], we have that each eigenspace E([[??].sub.k]), k [greater than or equal to] 1, exhibits the "unique continuation property", that is, if u [member of] E([[??].sub.k]) and u vanishes on a set of positive Lebesgue measure, then u [equivalent to] 0.