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中文摘要：
讨论黎曼-斯蒂尔切斯（R-S）积分的存在性问题，在文[1]基础上给出了R-S积分存在性的一个等价命题及其证明。在大学数学专业课程设置中，由于受到课时的限制，R-S积分内容讲授往往较难把握，不利于这部分内容的教与学。该研究结果不管是对于正确理解和应用R-S积分，还是对进一步学习数学其他专门化课程都有重要意义。
英文摘要：
Here Riemarm-Stieltjes（ R-S ） integral is concerned with. As it is well-known, this type of integral is an important generalization to Riemarm integral. Our purpose is to investigate of R-S integrality and give a new proof of the theorem by introducing some properties of bounded variation function. As a result, we establish the sufficient and necessary conditions of the existence theorem of R-S integral. Since class period is limited in the university calculus course, there is some substantial difficulty on teaching and studying such topic. The students of mathematics department may not understand the conceptions on R-S integral well. So our work will be helpful to them and all who are interested in the topic.
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