Category:Definitions/Step Functions

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This category contains definitions related to Step Functions.
Related results can be found in Category:Step Functions.

A real function $f: \R \to \R$ is a step function if and only if it can be expressed as a finite linear combination of the form:

$\map f x = \lambda_1 \chi_{\mathbb I_1} + \lambda_2 \chi_{\mathbb I_2} + \cdots + \lambda_n \chi_{\mathbb I_n}$


$\lambda_1, \lambda_2, \ldots, \lambda_n$ are real constants
$\mathbb I_1, \mathbb I_2, \ldots, \mathbb I_n$ are open intervals, where these intervals partition $\R$ (except for the endpoints)
$\chi_{\mathbb I_1}, \chi_{\mathbb I_2}, \ldots, \chi_{\mathbb I_n}$ are characteristic functions of $\mathbb I_1, \mathbb I_2, \ldots, \mathbb I_n$.


This category has only the following subcategory.

Pages in category "Definitions/Step Functions"

The following 3 pages are in this category, out of 3 total.