In mathematical analysis, the uniform norm (or sup norm) assigns, to real- or complex-valued bounded functions ⁠ f {\displaystyle f} ⁠ defined on a set...

In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance...

}(A,B)=\|h_{A}-h_{B}\|_{\infty }} where, on the right hand side, the uniform norm on the unit sphere is used. The properties of the support function as...

bounded real or complex-valued functions over X with the uniform norm topology, with the uniform metric defined by d ( f , g ) = ‖ f − g ‖ ∞ = sup x ∈ X...

is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The theorem was first published in 1927 by Stefan Banach...

mathematics, in the field of additive combinatorics, a Gowers norm or uniformity norm is a class of norms on functions on a finite group or group-like object which...

{\displaystyle C(\mathbb {R} )} continuous functions endowed with the uniform norm topology C c ( R ) {\displaystyle C_{c}(\mathbb {R} )} continuous functions...

using polynomials when the merit function is the maximum difference (uniform norm). Its discovery is attributed to Chebyshev. Let f {\displaystyle f} be...

itself a Banach space under the uniform norm. The uniform limit theorem also holds if continuity is replaced by uniform continuity. That is, if X and Y...

Mathematically, the Chebyshev distance is a metric induced by the supremum norm or uniform norm. It is an example of an injective metric. In two dimensions, i.e...

a normed space with norm defined by ‖ f ‖ = sup x ∈ X | f ( x ) | , {\displaystyle \|f\|=\sup _{x\in X}|f(x)|,} the uniform norm. The uniform norm defines...

{\displaystyle L^{\infty }} -norm or maximum norm (or uniform norm) is the limit of the L p {\displaystyle L^{p}} -norms for p → ∞ {\displaystyle p\to...

A social norm is a shared standard of acceptable behavior by a group. Social norms can both be informal understandings that govern the behavior of members...

tensor norm is defined to be a finitely generated uniform crossnorm. The projective cross norm π {\displaystyle \pi } and the injective cross norm ε {\displaystyle...

_{n=0}^{\infty }f_{n}(x)} is called normally convergent if the series of uniform norms of the terms of the series converges, i.e., ∑ n = 0 ∞ ‖ f n ‖ := ∑ n...

the uniform norm. Namely, for each continuous function φ : I a ( t 0 ) → B b ( y 0 ) , {\displaystyle \varphi :I_{a}(t_{0})\to B_{b}(y_{0}),} the norm of...

0:|f(x)|\leq C{\text{ for almost every }}x\}.} This norm is the uniform norm, it is an L p {\displaystyle L^{p}} norm for p = ∞ . {\displaystyle p=\infty .} The...

on a compact Hausdorff space with respect to its uniform norm, then it is bounded in the uniform norm on C(X) and in particular is pointwise bounded. Let...

separable. Let X be a compact Hausdorff space, and equip C(X) with the uniform norm, thus making C(X) a Banach space, hence a metric space. Then Arzelà–Ascoli...

value symbols stand for a metric for the space of solutions such as the uniform norm. Similar definitions also apply for non-grid discretization schemes such...

approximations by functions in a Chebyshev space that are the best in the uniform norm L∞ sense. It is sometimes referred to as Remes algorithm or Reme algorithm...

0430357} yields the optimal approximation (the best in the sense of the uniform norm of the error). However, this value is not used by the algorithm as it...

(1925) defined the uniformly almost-periodic functions as the closure of the trigonometric polynomials with respect to the uniform norm ‖ f ‖ ∞ = sup x |...

every algebra norm on C(X) is equivalent to the usual uniform norm. (Kaplansky himself had earlier shown that every complete algebra norm on C(X) is equivalent...

functional analysis, a uniform algebra A on a compact Hausdorff topological space X is a closed (with respect to the uniform norm) subalgebra of the C*-algebra...

the image of the unit ball is relatively compact in C([a,b]) with the uniform norm and a fortiori in L2[a,b]. Now apply the spectral theorem for compact...

{\displaystyle [-\pi ,\pi ]} with the uniform norm. This is the content of the Weierstrass theorem on the uniform density of trigonometric polynomials...

continuous functions on [ a , b ] {\displaystyle [a,b]} endowed with the uniform norm and with values in the space C [ c , d ] {\displaystyle C[c,d]} with...

E | f ( t ) | {\displaystyle \|f\|:=\sup _{t\in E}|f(t)|} denote the uniform norm on functions on E {\displaystyle E} . Define the Skorokhod metric σ {\displaystyle...

dense in the space of continuous functions on the unit circle, with the uniform norm; this is a special case of the Stone–Weierstrass theorem. More concretely...