【摘要】 累次极限与重极限的关系是数学分析课程多元函数部分的一个难点.受积分中Darboux上、下和的启发，引入弱累次极限的概念，概念减弱了累次极限交换次序的条件.并且建立了弱累次极限与重极限之间更为直接的关系，也就是可以用重极限来判别弱累次极限的存在性，也可以用弱累次极限来判别重极限的存在性.本文的结论有助于拓展学生的数学思维，从而能提升数学分析的教学质量.更多还原

【Abstract】 The relationship between repeated limits and double limits is a difficult point in mathematical analysis course. Motivated by Darboux upper sum and Darboux lower sum in integration, the paper introduces concept of weak repeated limits. The concept weakens the condition for exchanging order in repeated limits. Moreover, the paper establishes more direct relationship between repeated limits and double limits, i.e. double limits can be used to give the existence of weak repeated limits and weak repeated limits can be applied to find the existence of double limits. The results of this paper are helpful for expanding student’s mathematical thinking and can improve the teaching quality of mathematical analysis.更多还原