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Math Help - Measurable subsets

  1. #1
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    Measurable subsets

    If f and g are 2 measurable functions defined on a measurable subset E of R, then show that

     E_{1}=\{ x \in E : f(x) < g(x)\} is also measurable and
     E_{2} = \{ x \in E : f(x) = g(x)\} is measurable
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  2. #2
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    Let h:=f-g. Then your second problem is equivalent to showing \{ x\in E : h(x) = 0\} is measurable. But this is h^{-1}(0) and since h is measurable, and {0} is measurable, E_2 is too. Use similar ideas for E_1.
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