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The Definite Integral of Summable Functions

In: Lebesgue’s Theory of Integration

Author

Listed:
  • Rahul Jain

    (Indian Institute of Science (IISc), Indian Police Service
    Tata Institute of Fundamental Research (TIFR))

Abstract

The classical applications of integration of continuous functions, as well as the previous applications of integration in the sense of Riemann or in the sense of Duhamel and Serret, are sufficient to highlight the role of certain simple properties resulting from all the definitions of the integral we have already studied. They also serve to convince us that these properties must necessarily belong to the integral, if we want some analogy to be there between this integral and the integral of the continuous functions.

Suggested Citation

  • Rahul Jain, 2025. "The Definite Integral of Summable Functions," Springer Books, in: Lebesgue’s Theory of Integration, chapter 0, pages 131-159, Springer.
    • Handle: RePEc:spr:sprchp:978-981-96-1169-0_8
    DOI: 10.1007/978-981-96-1169-0_8
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