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Math Help - Riemann integrable relations

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    Riemann integrable relations

    Decide whether the statement is true (prove it) or false (provide counterexample).

    If f,g,h : [a,b] \rightarrow R are such that f(x) \leq g(x) \leq h(x) for all x \in [a,b] and f and h are Riemann integrable on [a,b], then so is g.
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    Quote Originally Posted by thaopanda View Post
    Decide whether the statement is true (prove it) or false (provide counterexample).

    If f,g,h : [a,b] \rightarrow R are such that f(x) \leq g(x) \leq h(x) for all x \in [a,b] and f and h are Riemann integrable on [a,b], then so is g.

    False: take f(x)=0\,,\,h(x)=1\,,\,g(x)=Dirichlet's\,\,\,functi  on.

    Tonio
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