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Math Help - measure theory

  1. #1
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    Lightbulb measure theory

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  2. #2
    Super Member Rebesques's Avatar
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    What is the sequence (g_n) needed for?
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  3. #3
    Super Member Rebesques's Avatar
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    Ok, I think you mean f_ng_n\rightarrow fg in the second one.

    For the first one, write

    f_n^2=(f_n-f+f)^2=(f_n-f)^2+2(f_n-f)f+f^2

    and note that f_n-f\rightarrow 0 in measure.

    For the second one, note

    (f_n+g_n)^2\rightarrow (f+g)^2

    by part 1, and expand the squares.
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