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@jemoka / Jemoka Knowledge Base / wiki/concepts/extended_value_extension.md
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--- title: "extended-value extension" type: concept related: [Extended Value Extension] source: https://www.jemoka.com/posts/kbhextended_value_extension/ confidence: high status: active --- Suppose \(f\) is convex on \(\mathbb{R}^{n}\), with domain \(\text{dom } f\). We can make an extended-value extension: \begin{equation} \tilde{f} \qty(x) = \begin{cases} f\qty(x), x \in \text{dom }f \\ \infty, \text{ otherwise } \end{cases} \end{equation} This could simplify notation .