# Definition:Distribution Space

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## Definition

Let $\map \DD {\R^d}$ be the test function space.

Let $T: \map \DD {\R^d} \to \C$ be a distribution.

Then the set of all $T$ is called the **distribution space** and is denoted by $\map {\DD'} {\R^d}$.

## Sources

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- 2017: Amol Sasane:
*A Friendly Approach to Functional Analysis*... (previous) ... (next): Chapter $\S 6.1$: A glimpse of distribution theory. Test functions, distributions, and examples