# Math Help - Riemann integrable relations

1. ## 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.

2. Originally Posted by thaopanda
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