论文标题
积分积分的基本定理：伏特拉的概括应用于平面功能
The Fundamental Theorem of Integral Calculus: a Volterra's generalization applied to flat functions
论文作者
论文摘要
在最近的论文中[5]平滑函数f：[0; 1] - > r，所有衍生物在0处的消失都被考虑，并且已经提出了F的全球状况，表明F确实是相同的0。本说明的目的是替换Riemann积分的微积分的经典基本定理，因为它已在[5]中使用，并且较弱的形式可以追溯到Volterra [7]，这鲜为人知。因此，从教学的角度来看，我们在本文中提出的证据也很重要，只要在文献中，很少有示例明确地出现了函数的下积分和上部积分（通常是假设函数是可riemann-noctegent的假设）。
In a recent paper [5] a smooth function f : [0; 1] --> R with all derivatives vanishing at 0 has been considered and a global condition, showing that f is indeed identically 0, has been presented. The purpose of this note is to replace the classical Fundamental Theorem of Calculus for the Riemann integral, as it has been used in [5], with a weaker form going back to Volterra [7], which is little known. Therefore the proof we propose in this paper turns to be important also from the teaching point of view, as long as in literature there are very few examples in which explicitly the lower integral and the upper integral of a function appear (usually the assumption that the function is Riemann-integrable is required).
