Continuous Real Function has Riemann Integral

Theorem

Let $f$ be a real function which is continuous on the closed interval $\closedint a b$.

Then $f$ is Riemann integrable over $\closedint a b$.


Proof


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Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): integration
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): integration
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