article
The extension of measures
International Journal of Statistics and Applied Mathematics · 2017 · Vol. 2(5) · pp. 101–103
Abstract
In this paper we have to show that if A is any algebra of subsets of a set X and if μ is a measure defined on A then there exist a σ- algebra A^* containing A and a measure μ^* defined on A^* such that μ^* (E)=μ(E) in A. In other words the measure μ can be extended to a measure on a σ-algebra A^* of subsets of X, which contains A.
Advanced Algebra and LogicAdvanced Topology and Set TheoryRings, Modules, and AlgebrasMeasure (data warehouse)MathematicsExtension (predicate logic)Set (abstract data type)Algebra over a fieldσ-finite measureDiscrete mathematicsPure mathematicsProbability measureComputer science
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