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...

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

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

is almost everywhere pointwise convergent to a function then the sequence converges in L 1 {\displaystyle L_{1}} to its pointwise limit, and in particular...

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

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...

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

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...

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

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

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

define pointwise Cauchy convergence, uniform convergence, and uniform Cauchy convergence of the sequence. Pointwise convergence implies pointwise Cauchy...

-topology on F {\displaystyle F} is called the topology of pointwise convergence. The topology of pointwise convergence on F {\displaystyle F} is identical to...

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

producing bounds on the CDF, we must differentiate between pointwise and simultaneous bands. A pointwise CDF bound is one which only guarantees their Coverage...

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

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

to turn a sequence space into a Fréchet space, namely the topology of pointwise convergence. Thus the name coordinate space because a sequence in an FK-space...

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...

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...

is a result that says, heuristically, whenever certain curvatures are pointwise constant then they are forced to be globally constant. The proof is essentially...

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

a group of loops in a topological group G with multiplication defined pointwise. In its most general form a loop group is a group of continuous mappings...

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

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

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...

bishop moves pointwise. It can also move one step edgewise. The queen moves as a rook and bishop. The king moves one step edgewise or pointwise. There is...

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