measure theory wikipedia - EAS
- measure theory (plural measure theories) (mathematics) A branch of mathematical analysis, concerned with the theory of integration, that generalizes the intuitive notions of length, area and volume.en.wiktionary.org/wiki/measure_theory
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Measure (mathematics) - Wikipedia
In mathematics, the concept of a measure is a generalization of common notions such as mass, distance/length, area, volume, probability of events, and — after some adjustments — electrical charge. These seemingly distinct concepts are innately very similar and may, in many cases, be treated as
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Xem thêmLet X be a set and Σ a σ-algebra over X. A function μ from Σ to the extended real number line is called a measure if it satisfies the following properties:
• Non-negativity: For all E in Σ, we have μ(E) ≥ 0....
Xem thêmSome important measures are listed here.
• The counting measure is defined by μ(S) = number of elements in S.
• The Lebesgue measure on ℝ is a complete translation-invariantmeasure...
Xem thêmLet μ be a measure.
Monotonicity
If E1 and E2 are measurable sets with E1 ⊆ E2 then
Measure of countable...
Xem thêmFor certain purposes, it is useful to have a "measure" whose values are not restricted to the non-negative reals or infinity. For instance, a countably
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Xem thêmIf the axiom of choice is assumed to be true, it can be proved that not all subsets of Euclidean space are Lebesgue measurable; examples of such sets include the Vitali set, and the non-measurable sets postulated by the Hausdorff paradoxand
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