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...

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

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

{\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...

functions: the pointwise, pairwise, and listwise approach. In practice, listwise approaches often outperform pairwise approaches and pointwise approaches...

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

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

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...

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...

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...

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}}...

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

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

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

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...

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...

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

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

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

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

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

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

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...

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....

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

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...

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