Fie \( f:[0,1]\to [0, \infty) \) o functie integrabila si convexa astfel incat
\( \int_0^1f(x)dx=0 \).
Sa se arate ca \( f(x)=0,\forall x\in (0,1) \).
Functie integrabila, convexa si cu integrala nula => f=0
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Functie integrabila, convexa si cu integrala nula => f=0
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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