Category:Simple Functions

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This category contains results about Simple Functions.

Let $\struct {X, \Sigma}$ be a measurable space.

A real-valued function $f: X \to \R$ is said to be a simple function if and only if it is a finite linear combination of characteristic functions:

$\ds f = \sum_{k \mathop = 1}^n a_k \chi_{S_k}$

where $a_1, a_2, \ldots, a_n$ are real numbers and each of the sets $S_k$ is $\Sigma$-measurable.