从依测度收敛到几乎处处收敛的教学设计探讨

Discussion on Teaching Design from Measure Convergence to Almost Everywhere Convergence

结合教育部对师范专业认证的指标,以及多年从事实变函数的课堂教学经验,本文主要探讨对mE=∞和mE=∞时的依测度收敛的可测函数列,如何逐步引导学生添加合适的条件得到几乎处处收敛。通过此研究有助于引导师范生如何深挖教材,如何通过串联间知识点间的联系设计来试题,从而达到培养师范生教学技能。

Based on the standards of the Ministry of Education for Teacher Education Certification, and the teaching experience of many years in the classroom, this paper mainly discusses the measurable function series converging with the measure convergence when mE=∞ and mE=∞, how to guide students to add appropriate conditions to derive the almost everywhere convergence. Through this research, it is helpful to guide students of normal university how to dig deep into teaching materials, how to design test questions by connecting knowledge points in series, so as to train teaching skills of students of normal university.