Search results

...y to use some special comparison functions. Class <math>\mathcal{K}</math> functions belong to this family: '''Definition''': a continuous function <math>\alpha : [0, a) \rightarrow [0, \infty)</math> is said to be ...

...scription|Two continuous functions can be glued together to create another continuous function}} ...tinuous function. The [[lemma (mathematics)|lemma]] is implicit in the use of [[piecewise function]]s. For example, in the book ''Topology and Groupoids' ...

{{Short description|Definition of cliquish function}} ...nuous function]] and [[quasi-continuous function]]. All (quasi-)continuous functions are cliquish but the converse is not true in general. ...

{{Short description|Mathematical concept in measure theory}} .... |last2=Gariepy |first2=R.F. |title=Measure theory and fine properties of functions |publisher=CRC Press |series=Studies in Advanced Mathematics |location=Boca ...

{{Short description|Concept in game theory}} ...[continuous function|continuity]] that finds application in the study of [[continuous game]]s. ...

...' if, for every [[computable sequence]] <math>\{x_i\}_{i=1}^\infty</math> of [[real number]]s, the [[sequence]] <math>\{f(x_i) \}_{i=1}^\infty</math> i ...<math>f \colon \mathbb{R} \to \mathbb{R}</math> is ''effectively uniformly continuous'' if there exists a [[primitive recursive function|recursive function]] <m ...

...ctions <math>\scriptstyle \scriptstyle\sin^n(x)</math> converge to the non-continuous red function. This can happen only if convergence is not uniform.]] ...convergence|uniform limit]] of any sequence of [[continuous function]]s is continuous. ...

{{Group theory sidebar}} ...t to each variable considered separately. It is a weakening of the concept of a [[topological group]]; all topological groups are semitopological groups ...

...'''pregaussian class''' or '''pregaussian set''' of functions is a set of functions, [[square integrable]] with respect to some [[probability measure]], such t ...(S)</math> a [[Set theory|set]] of square integrable with respect to ''P'' functions <math>f:S\to R</math>, that is ...

{{Short description|Continuous probability distribution}} ...arametric Estimation of a Multivariate Probability Density |journal=Theory of Probability & Its Applications |date=January 1969 |volume=14 |issue=1 |page ...

...Arthur Rosenthal]] and has been widely applied, particularly in [[operator theory]]. ...complex-valued function on ''K'' can be uniformly approximated by rational functions. ...

...<math>f</math> can be written as <math>f=g|f|</math> for some real-valued continuous function <math>g</math>. When dealing with [[compact space]]s, the two conc [[Rickart space]]s and the [[corona set]]s of locally compact σ-compact Hausdorff spaces are sub-Stonean spaces. ...

...th>L^{\lambda,p}(\Omega)</math> are [[Hölder condition|Hölder continuous]] functions over the domain <math>\Omega</math>. The [[seminorm]] of the Morrey spaces is given by ...

...mb|right|[[Mass]] measured in [[gram]]s is a function from this collection of weight to [[positive number|positive]] real numbers. The term "[[weight fun {{Functions}} ...

{{short description|Continuous closed surjective map, each of whose fibers are also compact sets}} ...locally compact space|local compactness]] that are not always preserved by continuous maps. ...

...that gives rise to a [[reproducing kernel]] on a natural [[Hilbert space]] of [[holomorphic function]]s. It is named for its discoverer, the Hungarian m ...e boundary. The [[Poisson integral]] implies that each element ''&fnof;'' of ''H''²(∂&Omega;) extends to a holomorphic function ''P&fnof;'' i ...

...with the construction of the [[Lyapunov function]] to prove the stability of a [[dynamical system]].<ref name=Khalil2001>{{Citation ...ynamical systems, where a common Lyapunov function describes the stability of multiple modes and switching signals. ...

...X),</math> is a [[vector space]] with respect to the pointwise addition of functions and scalar multiplication by constants. It is, moreover, a [[normed space] .... The uniform norm defines the [[topology]] of [[uniform convergence]] of functions on <math>X.</math> The space <math>\mathcal{C}(X)</math> is a [[Banach alg ...

{{short description|Says when particular class of games on the unit square has a mixed value}} ...istributions with respect to the [[Lebesgue measure]] (in other words, one of the players is forbidden to use a [[pure strategy]]). ...

...]] of ''f'' with respect to ''&mu;'' is "as big as it can be". The theory of maximising measures is relatively young and quite little is known about the ...t]] and [[metrizable]], Inv(''T'') is non-empty.) Define, for continuous functions ''f''&nbsp;:&nbsp;''X''&nbsp;→&nbsp;'''R''', the maximum integral function ...