اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Daniell Integral
166
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The basic properties of the Daniell integral are presented. We do not use the standard approach of introducing auxiliary spaces of the over-functions and under-functions. Instead, we use a simple and direct approach based on approximating integrable functions by absolutely convergent series of simple functions.
قيم البحث
اقرأ أيضاً
In this article we discuss a relation between the string topology and differential forms based on the theory of Chens iterated integrals and the cyclic bar complex.
The theory of integration over R is rich with techniques as well as necessary and sufficient conditions under which integration can be performed. Of the many different types of integrals that have been developed since the days of Newton and Leibniz,
one relative newcomer is that of the Henstock integral, aka the Henstock-Kurzweil integral, Generalized Riemann integral, or gauge integral, which was discovered independently by Henstock and Kurzweil in the mid-1950s. In this paper, we develop an alternative, sequential definition of the Henstock integral over closed intervals in R that we denote as the Sequential Henstock integral. We show its equivalence to the standard epsilon-delta definition of the Henstock integral as well as to the Darboux definition and to a topological definition of the Henstock integral. We then establish the basic properties and fundamental theorems, including two convergence theorems, for the Sequential Henstock integral and offer suggestions for further study.
Given a two-variable function f without critical points and a compact region R bounded by two level curves of f, this note proves that the integral over R of fs second-order directional derivative in the tangential directions of the interceding level
curves is proportional to the rise in f-value over R. Also discussed are variations on this result when critical points are present or R becomes unbounded.
This note concerns the general formulation by Preiss and Uher of Kestelmans influential result pertaining the change of variable, or substitution, formula for the Riemann integral.
In this paper, we prove a new integral representation for the Bessel function of the first kind $J_mu(z)$, which holds for any $mu,zinmathbb{C}$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
