# Definition:Heaviside Step Function/Two Variables

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## Definition

Let $u: \R \to \R$ be the Heaviside step function.

Then the **Heaviside step function of two variables** is the real function $u : \R^2 \to \R$ defined as the product of two step functions of one variable:

- $\map u {x, y} := \map u x \map u y$

In other words:

- $\map u {x, y} := \begin{cases} 1 & : \paren {x > 0} \land \paren {y > 0} \\ 0 & : \text {otherwise} \end{cases}$

## Source of Name

This entry was named for Oliver Heaviside.

## Sources

- 2017: Amol Sasane:
*A Friendly Approach to Functional Analysis*: Chapter $\S 6.2$: A glimpse of distribution theory. Derivatives in the distributional sense