Hi all,

If $\displaystyle f,g $ and $\displaystyle h$ are 3 continous functions on a set A,

that verify:

$\displaystyle \sup({f(t),t\in A})<\sup({h(t),t\in A})+\sup({g(t),t\in A})$

(beware the $\displaystyle <$ and not $\displaystyle \leq$)

can I say that there exists $\displaystyle x\in A$ such that:

$\displaystyle f(x)<g(x)+h(x)$

thank you

Deubelte