Can Expectations of Random Variables be Proven to Follow a Certain Pattern?

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If X is a random variable and f, g are functions is it possible to prove that:

E[f(X)] > E[g(X)] \Rightarrow \exists x: f(x) > g(x)
 
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Yes. Assume it is not true, g ≥ f for all x => E(g) ≥ E(f).
 

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