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.
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A Lebesgue measurable function A is a (q, N)-atom for [H.
If 1/q - 1/r < [mu] [less than or equal to] 1/q, then for any Lebesgue measurable function a satisfying
A is [Laplace] [cross product] B measurable if A belongs to the [sigma]--algebra generated by all sets of the form J x D, where J is Lebesgue measurable in I and D is Borel measurable in R.
The function u: J [right [arrow] U, is the control function which is a Lebesgue measurable where U = [0, a].
s](T,Z) the space of all (equivalence classes of) strongly Lebesgue measurable functions w : T [right arrow] Z such that t [right arrow] [[parallel]w(t)[parallel].
alpha]] (t) is Lebesgue measurable for any [alpha] [member of] [0,1].
The intersection with a Bernstein set has cardinality c also for sets in other rather wide perfect-saturated classes, such as Lebesgue measurable sets with positive measure or non-meagre sets with the property of Baire.
A] of a Lebesgue measurable set A is defined and several properties of [g.
n]) of Lebesgue measurable subsets of R such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Accordingly we can have a sequence of Lebesgue measurable subsets of R such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
In the general case of any Lebesgue measurable function f with bounded variation M > 0 the inequality of Lemma 3.
M,[omega]] (T) the class of Lebesgue measurable functions f : T [right arrow] C satisfying the condition