Corpus ID: 115717059

Theory of functions of a real variable

  title={Theory of functions of a real variable},
  author={Edwin Shields Hewitt and Kenneth A. Ross},
An algebra of generalized functions on an open interval; two-sided operational calculus
Let £2 be an open subinterval of the real line; suppose that OEQ. The purpose of this announcement is to describe an injection of L(fi) into a commutative algebra of operators. The injection is aExpand
Characterization of Finite/Fixed-time Stability of Evolution Inclusions
  • A. Polyakov
  • Mathematics, Computer Science
  • 2019 IEEE 58th Conference on Decision and Control (CDC)
  • 2019
Characterizations (necessary and sufficient con-ditions) of finite-time and fixed-time stability of evolution inclusions in Banach spaces are presented in terms of Lyapunov functionals.
Simplification and Strengthening of Weyl's Definition of Asymptotic Equal Distribution of Two Families of Finite Sets
Suppose that 1 < a < b < 1, au1nu2n � ··· � unnb, and av1nv2n � ··· � vnnb, n � 1. We simplify and strenghthen Weyl's definition of asymptotic equal distribution of U = {{uin} n=1}n�1 and V = {{vin}Expand
Derivatives: Why They Elude Classification
The purpose of this article is to examine, in the specific case of the class of derivatives, a problem that often arises when one studies a class of functions. The problem is that of characterizingExpand
Service in a Loop System
Two related measures of the grade of service are considered: the average queue length and the average v i r tua l wai t ing t ime at each s ta t ion. Expand
Space-filling Curves ReMittal
  • 2013
A 'continuous curve' in the plane is usually defined as the path traced by a moving point (x (t), Y (t)) as t runs over an interval of the real line, where x(-) and y(.) are continuous functions. TheExpand
Improvement paths in strategic games : A topological approach
An abstract theory of improvement dynamics for binary relations in metric spaces is developed, providing a general framework for studying various improvement relations and tâtonnement processes inExpand
Let « be a positive integer and F a function defined on a closed interval /. For x in /, let the «th approximate Peano derivative of F at x, if it exists, be denoted as F,nJx). For n = 1, theExpand
Maximizing a Binary Relation on Compact Subsets
The sets of maximal elements of a binary relation on compact subsets of a metric space deflne a choice function. Possibilities to characterize natural properties of the choice function (pathExpand
Circle Extensions of Zd-Rotations on the d-Dimensional Torus
Let T be an ergodic and free Z-rotation on the d-dimensional torus T given by T (m1,...,md)(z1, ..., zd) = (e1ddz1, ..., e d1dddzd), where (m1, ..., md) ∈ Z, (z1, ..., zd) ∈ T and [αjk]j,k=1...d ∈Expand