# Category:Piecewise Continuous Functions

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This category contains results about Piecewise Continuous Functions.

Definitions specific to this category can be found in Definitions/Piecewise Continuous Functions.

Let $f$ be a real function defined on a closed interval $\left[{a \,.\,.\, b}\right]$.

$f$ is **piecewise continuous** if and only if:

- there exists a finite subdivision $\left\{ {x_0, x_1, \ldots, x_n}\right\}$ of $\left[{a \,.\,.\, b}\right]$, where $x_0 = a$ and $x_n = b$, such that:

- for all $i \in \left\{ {1, 2, \ldots, n}\right\}$, $f$ is continuous on $\left({x_{i − 1} \,.\,.\, x_i}\right)$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Piecewise Continuous Functions"

The following 9 pages are in this category, out of 9 total.

### B

### P

- Piecewise Continuous Function does not necessarily have Improper Integrals
- Piecewise Continuous Function with Improper Integrals may not be Bounded
- Piecewise Continuous Function with One-Sided Limits is Bounded
- Piecewise Continuous Function with One-Sided Limits is Darboux Integrable
- Piecewise Continuous Function with One-Sided Limits is Uniformly Continuous on Each Piece