# Definition:Extended Real-Valued Function

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## Definition

Let $S$ be a set, and let $\overline \R$ denote the extended real numbers.

A mapping $f: S \to \overline \R$ is said to be an **extended real-valued function**.

## Also known as

Some authors refer to **extended real-valued functions** as **numerical functions**.

However, the adjective 'numerical' is misleading, and so using this convention is discouraged.

## Also see

## Sources

- 2005: René L. Schilling:
*Measures, Integrals and Martingales*... (previous) ... (next): $\S 8$