In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value f ( x ) {\displaystyle f(x)}...

In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than...

In statistics, probability theory and information theory, pointwise mutual information (PMI), or point mutual information, is a measure of association...

operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The...

uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions ( f n ) {\displaystyle (f_{n})} converges...

Riemann curvature tensor. A manifold M n {\displaystyle M^{n}} is called pointwise Osserman if, for every p ∈ M n {\displaystyle p\in M^{n}} , the spectrum...

{\displaystyle (S,\Sigma ,\mu )} . Suppose that the sequence converges pointwise to a function f {\displaystyle f} i.e. lim n → ∞ f n ( x ) = f ( x ) {\displaystyle...

set X into a vector space has a natural vector space structure given by pointwise addition and scalar multiplication. In other scenarios, the function space...

In mathematics, the lower envelope or pointwise minimum of a finite set of functions is the pointwise minimum of the functions, the function whose value...

equicontinuous and converges pointwise to a function (not necessarily continuous a-priori). In particular, the limit of an equicontinuous pointwise convergent sequence...

called pointwise limit, denoted x n , m → y m pointwise {\displaystyle x_{n,m}\to y_{m}\quad {\text{pointwise}}} , or lim n → ∞ x n , m = y m pointwise {\displaystyle...

provides an analogous example showing that polyhedral surfaces that converge pointwise to a curved surface do not necessarily converge to its area, even when...

turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication. All sequence spaces are linear...

Then: the sequence { g n ( x ) } n {\displaystyle \{g_{n}(x)\}_{n}} is pointwise non-decreasing at any x and g n ≤ f n {\displaystyle g_{n}\leq f_{n}}...

these confidence intervals constitute a 95% pointwise confidence band for f(x). In mathematical terms, a pointwise confidence band f ^ ( x ) ± w ( x ) {\displaystyle...

co-occurrence pointwise mutual information is a semantic similarity measure. To assess the degree of association between two given words, it uses pointwise mutual...

convergence in distribution of the sequence of random variables with pointwise convergence of their characteristic functions. This theorem is the basis...

kx\right)\end{aligned}}} These limits hold pointwise and in the sense of distributions. In general, however, pointwise convergence need not imply distributional...

(see microcontinuity). The formal definition and the distinction between pointwise continuity and uniform continuity were first given by Bolzano in the 1830s...

Rank approaches are often categorized using one of three approaches: pointwise (where individual documents are ranked), pairwise (where pairs of documents...

theorem is a fundamental result in mathematical analysis establishing the pointwise (Lebesgue) almost everywhere convergence of Fourier series of L2 functions...

to occur. Determination of convergence requires the comprehension of pointwise convergence, uniform convergence, absolute convergence, Lp spaces, summability...

Non-UI sequence of RVs. The area under the strip is always equal to 1, but X n → 0 {\displaystyle X_{n}\to 0} pointwise....

general relativity (also called a tetrad or vierbein) is a set of four pointwise-orthonormal vector fields, one timelike and three spacelike, defined on...

well. This theorem does not hold if uniform convergence is replaced by pointwise convergence. For example, let ƒn : [0, 1] → R be the sequence of functions...

In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number...

the sequence of corresponding characteristic functions {φn} converges pointwise to the characteristic function φ of X. Convergence in distribution is...

theorem says that if a monotone sequence of continuous functions converges pointwise on a compact space and if the limit function is also continuous, then...

In natural language processing and information retrieval, cluster labeling is the problem of picking descriptive, human-readable labels for the clusters...

{\displaystyle h_{\nu }=-\nabla \cdot \mathbf {F} _{\nu }} . They define (pointwise) monochromatic radiative equilibrium by ∇ ⋅ F ν = 0 {\displaystyle \nabla...