论文标题
位移
Displacements
论文作者
论文摘要
在这项工作中，我们基于新的位移概念建立了微积分理论。我们开发了从定义到微分方程的所有概念和结果，从拓扑，衡量并继续进行区分和集成开始。我们在途中发现了有趣的概念，例如相对于度量路径或位移导数的积分。我们通过微积分的基本定理将这两个概念中的两个概念联系起来。最后，我们开发了必要的框架，以通过将其与stieltjes微分方程联系起来来研究位移方程。
In this work we establish a theory of Calculus based on the new concept of displacement. We develop all the concepts and results necessary to go from the definition to differential equations, starting with topology and measure and moving on to differentiation and integration. We find interesting notions on the way, such as the integral with respect to a path of measures or the displacement derivative. We relate both of these two concepts by a Fundamental Theorem of Calculus. Finally, we develop the necessary framework in order to study displacement equations by relating them to Stieltjes differential equations.
