广义函数与无穷小
Generalized Functions and Infinitesimals
摘要：
半个世纪以来，人们普遍认为，在任何数学背景下，都不可能存在广义函数的非线性理论。本文的目的是表明相反的情况，并邀请读者参与辩论，并在一个意想不到的初级水平上检查其后果。这个悖论是关于数学中无穷小是否存在的历史争论的另一个例子，它与非标准分析有联系。本文是2006年6月在比萨举行的非标准分析会议上的一次讲话的书面版本。
英文摘要：
It has been widely believed for half a century that there will never exist a nonlinear theory of generalized functions, in any mathematical context. The aim of this text is to show the converse is the case and invite the reader to participate in the debate and to examine the consequences at an unexpectedly elementary level. The paradox appears as another instance of the historical controversy on the existence of infinitesimals in mathematics, which provides a connection with nonstandard analysis. This text is the written version of a talk at the meeting of Nonstandard Analysis, Pisa, june 2006.
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。
