Category:Definitions/Supremum Metric
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This category contains definitions related to Supremum Metric.
Related results can be found in Category:Supremum Metric.
Let $S$ be a set.
Let $M = \struct {A', d'}$ be a metric space.
Let $A$ be the set of all bounded mappings $f: S \to M$.
Let $d: A \times A \to \R$ be the function defined as:
- $\ds \forall f, g \in A: \map d {f, g} := \sup_{x \mathop \in S} \map {d'} {\map f x, \map g x}$
where $\sup$ denotes the supremum.
$d$ is known as the supremum metric on $A$.
Pages in category "Definitions/Supremum Metric"
The following 12 pages are in this category, out of 12 total.
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- Definition:Supremum Metric
- Definition:Supremum Metric on Bounded Real Functions on Closed Interval
- Definition:Supremum Metric on Bounded Real Sequences
- Definition:Supremum Metric on Bounded Real-Valued Functions
- Definition:Supremum Metric on Continuous Real Functions
- Definition:Supremum Metric on Differentiability Class
- Definition:Supremum Metric/Bounded Continuous Mappings
- Definition:Supremum Metric/Bounded Real Functions on Interval
- Definition:Supremum Metric/Bounded Real Sequences
- Definition:Supremum Metric/Bounded Real-Valued Functions
- Definition:Supremum Metric/Continuous Real Functions
- Definition:Supremum Metric/Differentiability Class