Skip to main content
SpringerLink
Log in

The Theory of Lebesgue Integral

  • Chapter
  • First Online:
Real Analysis on Intervals

  • 1796 Accesses

Abstract

In 1901, H. Lebesgue published the paper announcing the discovery of the integral that now bears his name.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Rudin, W.: Real and Complex Analysis, 3rd edn. McGraw-Hill Inc, New York (1987)

    MATH  Google Scholar 

  2. Ostrowski, A.M.: On some generalizations of the Cauchy-Frullani integral. Proc. Natl. Acad. Sci. U.S.A. 35, 612–616 (1949)

    Article  MATH  MathSciNet  Google Scholar 

  3. Vladimirov, V.S.: Equations of Mathematical Physics. Marcel Dekker, New-York (1971)

    Google Scholar 

  4. Hawkins, T.: Lebesgue’s Theory of Integration. Its Origins and Development, 2nd edn. AMS Chelsea Publishing, Providence (1975)

    Google Scholar 

  5. Folland, G.B.: Real Analysis: Modern Techniques and Their Applications, 2nd edn. Wiley, New York (1999)

    MATH  Google Scholar 

  6. Gordon, R.A.: The Integrals of Lebesgue, Denjoy, Perron and Henstock. Graduate Studies in Mathematics, vol. 4. American Mathematical Society, Providence (1994)

    MATH  Google Scholar 

  7. Hewitt, E., Stromberg, K.: Real and Abstract Analysis (Second printing corrected). Springer, Berlin (1969)

    Google Scholar 

  8. Lang, S.: Real and Functional Analysis, 3rd edn. Springer, New York (1993)

    Book  MATH  Google Scholar 

  9. Royden, H.L.: Real Analysis, 3rd edn. Macmillan, New York (1988)

    MATH  Google Scholar 

  10. Rudin, W.: Principles of Mathematical Analysis, 3rd edn. McGraw-Hill Book Co., New York (1976)

    MATH  Google Scholar 

  11. Willem, M.: Functional Analysis: Fundamentals and Applications. Birkhäuser, New York (2013)

    Book  Google Scholar 

  12. Chow, Y.S., Teicher, H.: Probability Theory: Independence, Interchangeability, Martingales, 3rd edn. Springer, New York (2003)

    MATH  Google Scholar 

  13. Maligranda, L.: Why Hölder’s inequality should be called Rogers’ inequality? Math. Inequal. Appl. 1, 69–83 (1998)

    MATH  MathSciNet  Google Scholar 

  14. Riesz, F.: Untersuchungen über Systeme integrierbarer Funktionen. Mathematische Annalen 69, 449–497 (1910)

    Article  MATH  MathSciNet  Google Scholar 

  15. Solovay, R.: A model of set theory in which every set of reals is Lebesgue measurable. Ann. Math. 92, 1–56 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  16. Wagon, S.: The Banach-Tarski Paradox. Cambridge University Press, Cambridge (1985)

    Book  MATH  Google Scholar 

  17. Oxtoby, J.: Measure and Category. Springer, New York (1971)

    Book  MATH  Google Scholar 

  18. Diamond, H., Gelles, G.: Interlaced second category sets. Am. Math. Mon. 92, 138–140 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  19. Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals, Series and Products, 5th edn. Academic Press, New York (2007)

    Google Scholar 

  20. Borwein, J.M., Bailey, D.H.: Mathematics by Experiment: Plausible Reasoning in the 21st Century. A. K. Peters, Natick (2004)

    Google Scholar 

  21. Widder, D.V.: The Laplace Transform. Princeton University Press, Princeton (1946)

    Google Scholar 

  22. Merkle, M.: Completely monotone functions—a digest (2 November 2012) arXiv:1211.0900

  23. Miller, K.S., Samko, S.G.: Completely monotonic functions. Integr. Transform. Spec. Funct. 12(4), 389–402 (2001)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abdus Salam School of Mathematical Sciences, Lahore, Pakistan

    A. D. R. Choudary

  2. Department of Mathematics, University of Craiova, Craiova, Romania

    Constantin P. Niculescu

Authors
  1. A. D. R. Choudary
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Constantin P. Niculescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. D. R. Choudary .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer India

About this chapter

Cite this chapter

Choudary, A.D.R., Niculescu, C.P. (2014). The Theory of Lebesgue Integral. In: Real Analysis on Intervals. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2148-7_11

Download citation

Publish with us

Policies and ethics

Search

Navigation