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Math Help - lebesque measurablity

  1. #1
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    lebesque measurablity

    m{\ast}A=0{\Rightarrow}m{\ast}(A{\cup}B)=m{\ast}B
    how can ı show this?
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by sah_mat View Post
    m{\ast}A=0{\Rightarrow}m{\ast}(A{\cup}B)=m{\ast}B
    how can ı show this?
    m{\ast}(A \cup B)+m {\ast}(A \cap B)=m{\ast}(A)+m{\ast}(B)

    but m{\ast}(A \cap B) \leq m{\ast}(A)=0 because A \cap B \subseteq A

    Since a measure is always positive, m{\ast}(A \cap B)=0


    Hence m{\ast}(A \cup B)=m{\ast}(A)+m{\ast}(B)=m{\ast}(B)
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  3. #3
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    thanks moo, ı have another question here;
    if E{\displaystyle1} and E{\displaystyle2} are measurable than m(E1{\cup}E2) +m(E1{\cap}E2)=m(E1)+m(E2)

    ı have an exam tomorrow so please answer as soon as possible
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