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## Homework Statement

Show that ##d(f,g) = \int_{0}^{1}\left | f(x) - g(x) \right | dx## is a distance function. Where ##f : [0,1] \rightarrow R## and ##f## is continuous.

## Homework Equations

## The Attempt at a Solution

I am stuck on the second property where you have to show d(f,g) = 0 iff f = g. THe left direction is trivial. However d(f,g) = 0 implying f=g is giving me trouble. I have tried contrapositive, but it doesnt seem to be getting me anywhere.