# 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.

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Simple Functions"

The following 16 pages are in this category, out of 16 total.

### M

### P

- Pointwise Difference of Simple Functions is Simple Function
- Pointwise Maximum of Simple Functions is Simple
- Pointwise Minimum of Simple Functions is Simple
- Pointwise Product of Simple Functions is Simple Function
- Pointwise Sum of Simple Functions is Simple Function
- Positive Part of Simple Function is Simple Function