Measure Theory and Integration By and For the Learner
Measure Theory and Integration By and For the Learner
复制标题
测量理论以及学习者的整合
DOI：
10.16929/sbs/2016.0005
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Aladji Babacar Niang
中科院分区：
文献类型：
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作者：
G. Lo;Aladji Babacar Niang
《测量理论与整合》一书旨在帮助初学者更好地掌握其本质。与在学术和垂直课程中提供内容相反，知识被分成练习，留给学习者解决。提示出现在任何角落，以帮助读者实现解决方案。通过这种方式，读者通过总结一个或一组练习的结果来构建知识。
每一章都被组织成包含知识的摘要文档、使学习者有机会通过练习自己提取知识的发现文档以及为练习提供详细答案的解决方案文档。少数结果(与非负函数积分定义的正当性有关的一个关键引理、Caratheodory定理和$\mathbb{R}^d$上的勒贝格-Stieljes测度)被列在附录文件中，供小组阅读。
完整的理论是以描述的方式呈现的。我们高度期望，任何学生通过材料，无论是单独或小组或在助理的监督下，将获得非常坚实的学科知识，顺便说一句，确保学习概率论，统计学，泛函分析等学科的良好基础。
这些材料已经在正常的真实分析课上成功地使用了几次。
Measure Theory and Integration is exposed with the clear aim to help beginning learners to perfectly master its essence. In opposition of a delivery of the contents in an academic and vertical course, the knowledge is broken into exercises which are left to the learners for solutions. Hints are present at any corner to help readers to achieve the solutions. In that way, the knowledge is constructed by the readers by summarizing the results of one or a group of exercises.
Each chapter is organized into Summary documents which contain the knowledge, Discovery documents which give the learner the opportunity to extract the knowledge himself through exercises and into Solution Documents which offer detailed answers for the exercises. Exceptionally, a few number of results (A key lemma related the justification of definition of the integral of a non-negative function, the Caratheodory's theorem and the Lebesgue-Stieljes measure on $\mathbb{R}^d$) are presented in appendix documents and given for reading in small groups.
The full theory is presented in the described way. We highly expect that any student who goes through the materials, alone or in a small group or under the supervision of an assistant will gain a very solid knowledge in the subject and by the way ensure a sound foundation for studying disciplines such as Probability Theory, Statistics, Functional Analysis, etc.
The materials have been successfully used as such in normal real analysis classes several times.