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The focus of this chapter is on introducing the Lebesgue measure on the real line. Starting from outer measure, it defines the Lebesgue measure of a set and proves its various properties. The construction of nonmeasurable sets is also given, and Vitali’s covering theorem is proved.

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Lebesgue Measure on Real Line

  • 章节

  • 发表日期：

    2025年

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  • Satya N. Mukhopadhyay,
  • Subhasis Ray

摘要

The focus of this chapter is on introducing the Lebesgue measure on the real line. Starting from outer measure, it defines the Lebesgue measure of a set and proves its various properties. The construction of nonmeasurable sets is also given, and Vitali’s covering theorem is proved.