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Thread: π-system and monotone class

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    π-system and monotone class




    Assume P is a π-system (that is, P is closed under finite intersections) and M is monotone class (that is M is a non-empty collection of subsets of Ω closed under monotone limits).

    Show that P⊂M does not imply σ(P)⊂M.

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    Re: π-system and monotone class

    The complement is not necessary in the monotone class?

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    Re: π-system and monotone class

    HI
    please more explain about question. thanks

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    Re: π-system and monotone class


    But I see a lots of reply in other forum

    http://math.stackexchange.com/questi...monotone-class

    I do not know much about the question, but my first thought is just construct a simple counter example.

    I mean that the sigma algebra is also closed under set complement, but not necessary closed in the monotone class and the pi system.

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