费马实数环上的微积分第一部分：积分学
Calculus in the ring of Fermat reals Part I: Integral calculus
摘要：
本文发展了费马实环上准标准光滑函数的积分学。该方法是通过证明原语的存在性和唯一性。除了经典的积分公式，我们还展示了费马空间的笛卡尔封闭框架处理无穷维积分算子的灵活性。标量之间的全序关系允许证明这些积分的几个经典的序性质，并研究Peano-Jordan-like积分域上的多重积分。
英文摘要：
We develop the integral calculus for quasi-standard smooth functions defined on the ring of Fermat reals. The approach is by proving the existence and uniqueness of primitives. Besides the classical integral formulas, we show the flexibility of the Cartesian closed framework of Fermat spaces to deal with infinite dimensional integral operators. The total order relation between scalars permits to prove several classical order properties of these integrals and to study multiple integrals on Peano-Jordan-like integration domains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
