$\displaystyle \int_{0}^{1}{|f-g|}=0 $

but

$\displaystyle \sup_{x\in[0,1]}{|f-g|}>0 $

f,g are two continuous functions on [0,1]

- Nov 3rd 2008, 11:13 AMszpengchaoare there two continuous functions in [0,1] satisfies these conditions
$\displaystyle \int_{0}^{1}{|f-g|}=0 $

but

$\displaystyle \sup_{x\in[0,1]}{|f-g|}>0 $

f,g are two continuous functions on [0,1] - Nov 3rd 2008, 12:28 PMPlato
You know that if $\displaystyle f\;\&\;g$ are continuous functions then $\displaystyle \left| {f - g} \right|$ is also a continuous function.

If a continuous function is positive at any point in $\displaystyle [0,1]$ then the function is positive throughout some subinterval.

What does that say about the integral?