Measure and integration Measurable functions Concept
Simple function
Summary
A simple function is a measurable function that takes only finitely many values. It is a finite combination of indicator functions of measurable sets, so its integral is a finite sum. The Lebesgue integral of a nonnegative function is defined by approximating it from below by simple functions.
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About this page
| Tag | 7WMBX7M4P6 |
|---|---|
| URI | m2://7WMBX7M4P6 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A20 |
| Specializes | Measurable function |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Strongly measurable function
- Bartle–Dunford–Schwartz integral
- Density of simple functions in Lp
- Integral of a non-negative function