What does uniform metric mean?
Definitions for uniform metric
uni·form met·ric
This dictionary definitions page includes all the possible meanings, example usage and translations of the word uniform metric.
Wiktionary
uniform metricnoun
The metric where f and g are functions on X.
Wikipedia
uniform metric
In mathematical analysis, the uniform norm (or sup norm) assigns to real- or complex-valued bounded functions f {\displaystyle f} defined on a set S {\displaystyle S} the non-negative number ‖ f ‖ ∞ = ‖ f ‖ ∞ , S = sup { | f ( s ) | : s ∈ S } . {\displaystyle \|f\|_{\infty }=\|f\|_{\infty ,S}=\sup \left\{\,|f(s)|:s\in S\,\right\}.} This norm is also called the supremum norm, the Chebyshev norm, the infinity norm, or, when the supremum is in fact the maximum, the max norm. The name "uniform norm" derives from the fact that a sequence of functions { f n } {\displaystyle \left\{f_{n}\right\}} converges to f {\displaystyle f} under the metric derived from the uniform norm if and only if f n {\displaystyle f_{n}} converges to f {\displaystyle f} uniformly.If f {\displaystyle f} is a continuous function on a closed and bounded interval, or more generally a compact set, then it is bounded and the supremum in the above definition is attained by the Weierstrass extreme value theorem, so we can replace the supremum by the maximum. In this case, the norm is also called the maximum norm. In particular, if x {\displaystyle x} is some vector such that x = ( x 1 , x 2 , … , x n ) {\displaystyle x=\left(x_{1},x_{2},\ldots ,x_{n}\right)} in finite dimensional coordinate space, it takes the form:
Numerology
Chaldean Numerology
The numerical value of uniform metric in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of uniform metric in Pythagorean Numerology is: 2
Translations for uniform metric
From our Multilingual Translation Dictionary
- metrik seragamIndonesian
- சீரான மெட்ரிக்Tamil
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"uniform metric." Definitions.net. STANDS4 LLC, 2024. Web. 25 Apr. 2024. <https://www.definitions.net/definition/uniform+metric>.
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