Continuous FunctionOptimal SequenceA proof of Rosenthal's co-index conjecture is given. Our approach uses optimal sequences of continuous functions converging to a Baire-1 function. Their existence is obtained by the "optimal sequences theorem" stated and proved here. For a sequence\\documentclass[...
9 RegisterLog in Sign up with one click: Facebook Twitter Google Share on Facebook piecewise (redirected fromPiecewise-continuous) piecewise (ˈpiːsˌwaɪz) adv 1.(Mathematics)mathswith respect to a number of discrete pieces 2.formalin pieces or by degrees ...
The Continuous Mapping theorem states that stochastic convergence is preserved by continuous functions. The problemSuppose that a sequence of random vectors converges to a random vector (in probability, in distribution or almost surely). Now, take a transformed sequence , where is a function. ...
Continuous functions have many important properties that account for the great importance of these functions in mathematics and applications. One of the most important properties is expressed in the theorem that states that for every function continuous on a closed interval[a, b], it is possible to...
Continuous functions are very important in the study of optimization problems. We can see that the extreme value theorem guarantees that within an interval, there will always be a point where the function has a maximum value. The same can be said for a minimum value. Many optimization algorithm...
摘要: In this paper we intend to find equivalent conditions under which continuous functions of a metric space are always uniformly continuous. Isiwata has attempted to prove a theorem in a recently published paper [3] by a method that has a close relation with ours. Unfortunately关键词:...
yielding a function from N into S is defined by the condition (Def. 1). (Def. 1) Let i be a natural number. Then (i) if there exists a natural number k such that i = 2 · k, then (a,b,...)(i) = a, and (ii) if it is not true that there exists a natural number ...
Absolutely continuous real-numbered functions are those functions for which the Fundamental Theorem of Calculus (FTC) holds [1]. In other words, absolute continuity identifies which functions can be antiderivatives: a function on a closed, bounded interval is absolutely continuous on that interval if...
We establish asymptotic equalities for upper bounds of the deviations of the de la Vallee-Poussin operators from functions of low smoothness belonging to the classes .关键词: Continuous Function Important Case Asymptotic Equality DOI: 10.1007/s11253-005-0204-9 ...
the latter establishes for a given medium the form of the relation among the stresses or their rates of change and the strains or their rates of change for the particles. The characteristics of the medium may also depend on the temperature and other physicochemical parameters; the form of these...