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Topic: Measurable set

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	Measure (mathematics) - Wikipedia, the free encyclopedia
		In mathematics, a measure is a function that assigns a number, e.g., a "size", "volume", or "probability", to subsets of a given set.
		A measure can be extened to a complete one by considering the σ-algebra of subsets Y which differ by a subset of a null set from a measurable set X, that is such that the symmetric difference of X and Y is contained in a null-set.
		The Haar measure for a locally compact topological group is a generalization of the Lebesgue measure and has a similar uniqueness property.
	en.wikipedia.org /wiki/Measure_(mathematics) (886 words)

	Measure (mathematics) - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-10-20)
		Measure theory is that branch of real analysis which investigates sigma algebras, measures, measurable functions and integrals.
		Formally, a measure μ is a function which assigns to every element S of a given sigma algebra X a value μ(S), a non-negative real number or ∞.
		A set in a measure space has σ-finite measure if it is a countable union of sets with finite measure.
	encyclopedia.learnthis.info /m/me/measure__mathematics_.html (755 words)

	Lebesgue measure
		Sets which can be assigned a volume are called Lebesgue measurable; the volume or measure of the Lebesgue measurable set A is denoted by λ(A).
		Countable unions and intersections of Lebesgue measurable sets are Lebesgue measurable.
		The Borel measure agrees with the Lebesgue measure on those sets for which it is defined; however, there are many more Lebesgue-measurable sets than there are Borel measurable sets.
	www.brainyencyclopedia.com /encyclopedia/l/le/lebesgue_measure.html (674 words)

	Read about Measure (mathematics) at WorldVillage Encyclopedia. Research Measure (mathematics) and learn about Measure ... (Site not responding. Last check: 2007-10-20)
		Formally, a countably additive measure μ is a
		is a sequence of pairwise disjoint sets in
		A measure space Ω is called finite if μ(Ω) is a finite real number (rather than ∞).
	encyclopedia.worldvillage.com /s/b/Measure_theory (713 words)

	Non-measurable set -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-20)
		When you increase in (The magnitude of something in a particular direction (especially length or width or height)) dimension the picture gets worse.
		As an added bonus, you get that even an infinite series of disjoint sets satisfies the sum formula, a property mathematicians call (Click link for more info and facts about σ-additivity) σ-additivity.
		A very short discussion of the reasons can be found in (Click link for more info and facts about measure (mathematics)) measure (mathematics).
	www.absoluteastronomy.com /encyclopedia/n/no/non-measurable_set.htm (567 words)

	Measures and outer measures (Site not responding. Last check: 2007-10-20)
		Outer and inner vanishing measures and division in $H^infty + C$, Keiji Izuchi...
		Performance Measures for OCS Operators and Form MMS-131...
		Measuring Inner and Outer Behavioral Effects of Hemi-Sync®...
	www.scienceoxygen.com /math/394.html (278 words)

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