Definition:Equicontinuous Real Functions
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Definition
Let $\family {f_i}_{i \mathop \in I}$ be an indexed family of real functions, where $I$ is an arbitrary index set.
Let each element of $\family {f_i}$ have the same domain.
Let $\family {f_i}$ have the property that:
- $\forall \epsilon \in \R_{>0}: \exists \delta \in \R_{>0}: \size {x_1 - x_2} < \delta \implies \size {\map {f_i} {x_1} - \map {f_i} {x_2} } < \epsilon$
for all $i \in I$.
Then $\family {f_i}_{i \mathop \in I}$ is a family of equicontinuous real functions.
Also see
- Results about equicontinuous real functions can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): equicontinuous functions
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): equicontinuous functions