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Let be a set. Let be a subset of the power set of Then, is a σ-algebra on the set if the following is true: 1. * ( is an element of .) 2. * (For any set, if a set is an element of , then its complement is in also.) 3. * (If there is a countable collection of sets that are elements of , then the union of those elements are also in ). If is a σ-algebra on the set , then is a measure space.

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  • Sigma-algebra
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  • Let be a set. Let be a subset of the power set of Then, is a σ-algebra on the set if the following is true: 1. * ( is an element of .) 2. * (For any set, if a set is an element of , then its complement is in also.) 3. * (If there is a countable collection of sets that are elements of , then the union of those elements are also in ). If is a σ-algebra on the set , then is a measure space.
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abstract
  • Let be a set. Let be a subset of the power set of Then, is a σ-algebra on the set if the following is true: 1. * ( is an element of .) 2. * (For any set, if a set is an element of , then its complement is in also.) 3. * (If there is a countable collection of sets that are elements of , then the union of those elements are also in ). If is a σ-algebra on the set , then is a measure space.
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