Measure space: Difference between revisions
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In [[mathematics]], a '''measure space''' is a triple <math>(\Omega,\mathcal{F},\mu)</math> where <math>\Omega</math> is a [[set]], <math>\mathcal{F}</math> is a [[sigma algebra]] of subsets of <math>\Omega</math> and <math>\mu</math> is a [[measure (mathematics)|measure]] on <math>\mathcal{F}</math>. If <math>\mu</math> satisfies <math>\mu(\Omega)=1</math> then the measure space is called a '''probability space'''. | In [[mathematics]], a '''measure space''' is a triple <math>\scriptstyle (\Omega,\mathcal{F},\mu)</math> where <math>\scriptstyle \Omega</math> is a [[set]], <math>\scriptstyle \mathcal{F}</math> is a [[sigma algebra]] of subsets of <math>\scriptstyle \Omega</math> and <math>\mu</math> is a [[measure (mathematics)|measure]] on <math>\scriptstyle \mathcal{F}</math>. If <math>\mu</math> satisfies <math>\scriptstyle \mu(\Omega)=1</math> then the measure space is called a '''probability space'''. | ||
==See also== | ==See also== | ||
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[[Measurable space]] | [[Measurable space]] | ||
[[Probability theory]] | [[Probability theory]][[Category:Suggestion Bot Tag]] | ||
Latest revision as of 06:01, 17 September 2024
In mathematics, a measure space is a triple where is a set, is a sigma algebra of subsets of and is a measure on . If satisfies then the measure space is called a probability space.
