Lebesgue Measure and Integration

  • Lebesgue.pdf
    This lecture notes is written for part of the course Real Analysis at Xi'an Jiaotong University.
    • Since students at the university take the course quite early in their studies, many of them require much guidence especially in writing proofs. Therefore, in the lectures notes, detail proofs together with their ideas are given.
    • The treatment of the materials is similar to that in most standard textbooks on Lebesgue Measure and Integration. One exception is that before introducing the concept of measurable sets, an example is given to show that the Lebesgue outer measure is non-additive. Usually, such an example is proved to be non-measurable using properties of measurable sets and such a proof is much simpler.
    • The following two topics, which are usually taught in a course on Real Anaylsis, are not discussed in the lecture notes:
      • Differentiation and Integration
      • Higher Dimensional Lebesgue Integration and Fubini's Theorem

  • Lebesgue_source.zip The zip file contains the source files (tex and other files) that are used to produce the lecture notes.