Step function: Difference between revisions

Revision as of 16:50, 27 February 2020

Revision as of 17:00, 27 February 2020

Line 11:

:<math>f(x) = \sum\limits_{i=0}^n \alpha_i \chi_{A_i}(x)</math>, for all real numbers <math>x</math>

where <math>n\ge 0</math> and, <math>\alpha_i</math> are real numbers, <math>A_i</math> are intervals, and <math>\chi_A</math> is the [[indicator function]] of <math>A\text{:}</math>:

:<math>\chi_A(x) = \begin{cases}

1 & \text{if } x \in A, \\

0 & \text{if } x \notin A. \\

\end{cases}</math>