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Corollary: Functions Continuous at a Point and Identical to Other Functions in a Neighborhood of This Point
(related to Definition: Continuous Functions at Single Real Numbers)
Let \(D\) be a subset of real numbers \(\mathbb R\), \(a\in D\), and let \(f,g:D\to\mathbb R\) be two function.
Let $f$ be continuous at $a$ and let it be identical to $g$ in a neighborhood of $a$, i.e. for an (arbitrarily small) positive real number $\epsilon > 0$, let $f(x)=g(x)$ for all $x$ with $a a\epsilon < x < a+\epsilon$. Then $g$ is continuous at $g$.
Table of Contents
Proofs: 1
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983