广义积分。第一部分

IF 1 Q1 MATHEMATICS

Formalized Mathematics Pub Date : 2021-12-01 DOI:10.2478/forma-2021-0019

N. Endou

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引用次数: 2

摘要

在本文中，我们使用Mizar系统处理黎曼反常积分[1]，[3]。Yamazaki等人在[5]中讨论了有限值的反常积分，但一般来说，反常积分不假设它们是有限的。因此，我们已经形式化了不将积分值限制为有限值的一般反常积分。另外，[5]中的每个定理都假定被积域包含一个闭区间，但由于反常积分要在半开区间上讨论，我们也对其进行了修正。

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Improper Integral. Part I

Summary In this article, we deal with Riemann’s improper integral [1], using the Mizar system [2], [3]. Improper integrals with finite values are discussed in [5] by Yamazaki et al., but in general, improper integrals do not assume that they are finite. Therefore, we have formalized general improper integrals that does not limit the integral value to a finite value. In addition, each theorem in [5] assumes that the domain of integrand includes a closed interval, but since the improper integral should be discusses based on the half-open interval, we also corrected it.

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来源期刊

Formalized Mathematics MATHEMATICS-

自引率

0.00%

发文量

审稿时长

10 weeks

期刊介绍： Formalized Mathematics is to be issued quarterly and publishes papers which are abstracts of Mizar articles contributed to the Mizar Mathematical Library (MML) - the basis of a knowledge management system for mathematics.