We introduce some properties (B) and (C) of functions of two variables such that (B) is an essential weakening of quasi-continuity and (C) is valid, in particular, for functions taking values in separable metriz
Any non-constant function from the plane to {0,1} is of necessity discontinuous. If you compose such a function with a path on which the function is constant, then the result is a constant function from (an interval of) the reals to {0,1}, which is continuous. Here the y-axis lie...
Mathematical ConceptsCollege MathematicsThis note considers functions of two variables which are continuous on a possibly unbounded closed region in |R2, and the functions of one variable obtained by integrating out the other variable over this region. The question of continuity of these functions is ...
These functions have the “smoothest” type of continuity, followed by uniform continuity and then plain old continuity. All absolutely continuous functions are continuous, but the converse is not true.Absolutely continuous functions and random variables are related to each other in the following way...
investigating the potential of computer environments for the teaching and learning of functions a double analysis from two research traditions 热度: Lower bound for the best approximations of periodic summable functions of two variables and their conjugates in terms of Fourier coefficients ...
approximation of the function of two (and more) variables (kernel) by means of degenerate function (kernel). We apply obtained results to the investigation of the local structure of random processes, for example, we find the necessary and sufficient condition for continuity of Gaussian and non-...
Let f, g be two continuous functions on D. Prove that the functions h(x) = min{f(x), g(x)} and H(x) = max{f(x),g(x)} are continuous on D. Are h and H uniformly continuous on D in f and g are? Prove that if...
are the simplest functions of a variablexthat are continuous for all values ofx. The sum, difference, and product of continuous functions again yield continuous functions. The quotient of two continuous functions is also a continuous function, except for those values ofxfor which the denominator va...
摘要: Order estimates are obtained for the approximations of the classes \( B_{p,heta }^\Omega \) of periodic functions of two variables in the space L q by operators of orthogonal projection and by linear operators satisfying certain conditions....
1. This paper mainly presents the problem for the continuity of function of several variables,and introduces some new methods to verify the continuity for multivariate functions. 本文主要讨论了多元函数的连续性问题,介绍了几种判定多元函数连续性的方法。