Lebesgue Integral
Vigirdas Mackevičius · 2014
This chapter provides the definition of a Cauchy sequence, or a fundamental sequence. To distinguish Cauchy sequences of step functions from Cauchy sequences of numbers, the former are called Cauchy sequences in the L1 sense or Cauchy sequences in the mean. The chapter provides the proof of the correctness of the definition of integral. Formulas are used to explain the following theorems: Beppo Levi theorem and Fatou-Lebesgue theorem. Proof of the Beppo Levi theorem and proof of the Fatou-Lebesgue theorem are discussed. A series of problems to be solved are provided at the end of the chapter.