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Math Help - signed measure

  1. #1
    GTO
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    signed measure

    For nonnegative f,g \in L^1(X,F,\mu) and sub \sigmaalgebra \Lambda which is not a subset of F, define v(A)=\int_A (f-g) d\mu for all A \in \Lambda.
    Show that v is a signed measure.

    i got confused here. since \Lambda is not a subset of F, how do i find the integral? can i integrate it only when A is an element of F?
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  2. #2
    GTO
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    Quote Originally Posted by GTO View Post
    For nonnegative f,g \in L^1(X,F,\mu) and sub \sigmaalgebra \Lambda which is not a subset of F, define v(A)=\int_A (f-g) d\mu for all A \in \Lambda.
    Show that v is a signed measure.

    i got confused here. since \Lambda is not a subset of F, how do i find the integral? can i integrate it only when A is an element of F?
    If A is not in F, then what is v(A)=\int_A (f-g) d\mu? is it zero or undefined?
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