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Thread: generated algebra

  1. #1
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    generated algebra

    Hi,

    can anybody explain me how to construct an algebra and \sigma-algebra generated by K, if K=\{\{x\}\mid x\in X\} and X - universal set.
    I guess it also depends on the fact whether X is finite or infinite, countable or uncountable, does it?
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  2. #2
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    Quote Originally Posted by waytogo View Post
    Hi,

    can anybody explain me how to construct an algebra and \sigma-algebra generated by K, if K=\{\{x\}\mid x\in X\} and X - universal set.
    I guess it also depends on the fact whether X is finite or infinite, countable or uncountable, does it?
    The algebra generated by K will be the finite subsets of X together with their complements. The \sigma-algebra generated by K will be the countable subsets of X together with their complements.
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