对公理化语言的扩展工具的一些思考，重点是概率论和Dirichlet形式的错误计算
Some thoughts upon axiomatized languages with estension tools, a focus on probability theory and error calculus with Dirichlet forms
摘要：
通过对20世纪发展起来的“随机序列理论”和Kolmogorov提出的概率论的公理化方法的比较，说明了sigma-可加性作为推广工具的重要性。同样，柯西准则似乎是数学分析的一个扩展工具。狄利克雷形式理论也拥有这样的扩展工具。它们是这些语言丰富的源泉，也是它们创造力的条件。这与所谓的理查德悖论有关。
英文摘要：
A comparison of the "theory of random sequences" developed during the twentieth century and the axiomatic approach of probability theory proposed by Kolmogorov shows the importance of sigma-additivity as extension tool. Similarly, the Cauchy criterion appears to be an extension tool for mathematical analysis. The Dirichlet forms theory possesses also such an extension tool. They are the source of the fruitfulness of these languages and the condition of their creativity. A connection is given with the so-called Richard paradox.
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。
