Definition:Piecewise Continuous Function/Variant 3
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Definition
Let $f$ be a real function defined on $\R$.
$f$ is piecewise continuous if and only if:
- for any closed interval $\closedint a b$:
- there exists a finite subdivision $\set {x_0, x_1, \ldots, x_n}$ of $\closedint a b$, where $x_0 = a$ and $x_n = b$, such that:
- for all $i \in \set {1, 2, \ldots, n}$, $f$ is continuous on $\openint {x_{i − 1} } {x_i}$.
Sources
- 1962: Richard Courant and David Hilbert: Methods of Mathematical Physics: Volume $\text {II}$ Partial Differential Equations: $\text {IV}$. Potential Theory and Elliptic Differential Equations: $\S 1$. Basic Notions: $2$. Potentials of Mass distributions: Footnote $2$, second paragraph