Concave Real Function is Continuous

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Theorem

Let $f$ be a real function which is concave on the open interval $\openint a b$.


Then $f$ is continuous on $\openint a b$.


Proof

From Concave Real Function is Left-Hand and Right-Hand Differentiable, $f$ is left-hand and right-hand differentiable on $\openint a b$.

From Left-Hand and Right-Hand Differentiable Function is Continuous, $f$ is continuous on $\openint a b$.

$\blacksquare$


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