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Math Help - every subset of a null set is also a null set

  1. #1
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    Exclamation every subset of a null set is also a null set

    I want proof of this statement

    "every subset of a null set is also a null set"...

    Where Null set is a set whose measure is 0
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  2. #2
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    Re: every subset of a null set is also a null set

    One of the conditions for a measure, m, is that if A\subseteq B then m(A)\le m(B).
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  3. #3
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    Re: every subset of a null set is also a null set

    Thanks a lot

    I want to ask another thing related to it that how can we prove

    Phy belongs to Rn

    Where Rn denotes all null subsets of algebra R
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  4. #4
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    Re: every subset of a null set is also a null set

    What do you mean by "Phy"?
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  5. #5
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    Re: every subset of a null set is also a null set

    greek work phy means null or empty...
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  6. #6
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    Re: every subset of a null set is also a null set

    Quote Originally Posted by awais100 View Post
    greek work phy means null or empty...
    It is phi [TEX]\Phi \phi[/TEX] gives \Phi~~  \phi
    That is a letter of the Greek alphabet it is not a Greek word, much less a work.

    In all the treatments of measure that I have seen the fact \mu(\emptyset)=0 is part of the definition of measure.
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  7. #7
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    Re: every subset of a null set is also a null set

    Sorry for the typo mistake

    Thanks
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  8. #8
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    Re: every subset of a null set is also a null set

    In any case the empty set is a subset of every set and certainly has measure 0, therefore is in Rn.
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