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Math Help - Finding the smallest sigma algebra containing two sets

  1. #1
    Junior Member gusztav's Avatar
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    Finding the smallest sigma algebra containing two sets

    Hello,

    the problem is the following: Let A, B \subseteq \Omega. Find the smallest \sigma-algebra ( \mathcal{F}) on \Omega containing the sets A and B.

    I have tried to answer this, and would appreciate if you could tell me if this the correct answer, or if I have left something out:

    \{ <br />
\emptyset, \Omega, A, B, A^c, B^c, A \cup B, A \cap B, A \Delta B , A \backslash B, B \backslash A, <br />
(A \cup B)^c, (A \cap B)^c, (A \Delta B)^c , (A \backslash B)^c, (B \backslash A)^c  \}

    Thanks!
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  2. #2
    Moo
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    A Cute Angle Moo's Avatar
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    Hello,

    It looks correct.
    Of course, if A=B or A\subset B or... there will be redundance.

    Anyway, if you want to be 'clearer', you can change the complements (using de Moivre's formula)
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