# uniformly

31

**Modulus of continuity**— In mathematical analysis, a modulus of continuity is a function used to measure quantitatively the uniform continuity of functions. So, a function admits ω as a modulus of continuity if and only if for all x and y in the domain of f. Since moduli …32

**Uniform convergence**— In the mathematical field of analysis, uniform convergence is a type of convergence stronger than pointwise convergence. A sequence {fn} of functions converges uniformly to a limiting function f if the speed of convergence of fn(x) to f(x) does… …33

**Arzelà–Ascoli theorem**— In mathematics, the Arzelà–Ascoli theorem of functional analysis gives necessary and sufficient conditions to decide whether every subsequence of a given sequence of real valued continuous functions defined on a closed and bounded interval has a… …34

**Uniform continuity**— In mathematical analysis, a function f ( x ) is called uniformly continuous if, roughly speaking, small changes in the input x effect small changes in the output f ( x ) ( continuity ), and furthermore the size of the changes in f ( x ) depends… …35

**Uniform absolute-convergence**— In mathematics, uniform absolute convergence is a type of convergence for series of functions. Like absolute convergence, it has the useful property that it is preserved when the order of summation is changed. Motivation A convergent series of… …36

**Uniform space**— In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and… …37

**Uniform integrability**— The concept of uniform integrability is an important concept in functional analysis and probability theory. If μ is a finite measure, a subset is said to be uniformly integrable if Rephrased with a probabilistic language, the definition… …38

**Sundial**— A sundial is a device that measures time by the position of the Sun. In common designs such as the horizontal sundial, the sun casts a shadow from its style (a thin rod or a sharp, straight edge) onto a flat surface marked with lines indicating… …39

**n-sphere**— 2 sphere wireframe as an orthogonal projection Just as a …40

**Equicontinuity**— In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood (a precise definition appears below). More generally, equicontinuous applies to any… …