are there two continuous functions in [0,1] satisfies these conditions

**szpengchao** · November 3rd 2008, 11:13 AM

$\int_{0}^{1}{|f-g|}=0$
but
$\sup_{x\in[0,1]}{|f-g|}>0$

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

**Plato** · November 3rd 2008, 12:28 PM

You know that if $f\;\&\;g$ are continuous functions then $\left| {f - g} \right|$ is also a continuous function.
If a continuous function is positive at any point in $[0,1]$ then the function is positive throughout some subinterval.
What does that say about the integral?

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