Skip to main content

Lebesgue Measure

  • Chapter
  • First Online:
Measure, Integral, Derivative

Part of the book series: Universitext ((UTX))

  • 4966 Accesses

Abstract

In this chapter we present elements of Lebesgue’s theory of measure and measurable functions.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Apostol, T.M.: Mathematical Analysis, 2nd edn. Addison-Wesley, Reading (1974)

    MATH  Google Scholar 

  2. Austin, D.: A geometric proof of the Lebesgue differentiation theorem. Proc. AMS 16, 220–221 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bartle, R., Sherbert, D.: Introduction to Real Analysis, 4th edn. Wiley, New York (2011)

    Google Scholar 

  4. Botsko, M.W.: An elementary proof of Lebesgue’s differentiation theorem. Am. Math. Mon. 110, 834–838 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bourbaki, N.: General Topology. Addison-Wesley, Reading (1966)

    Google Scholar 

  6. Halmos, P.: Naive Set Theory. Springer, New York (1974)

    MATH  Google Scholar 

  7. Knuth, D.E.: Problem E 2613. Am. Math. Mon. 83, 656 (1976)

    Article  MathSciNet  Google Scholar 

  8. Kreyszig, E.: Introductory Functional Analysis with Applications. Wiley, New York (1978)

    MATH  Google Scholar 

  9. Lebesgue, H.: Leconş sur l’intégration et la recherche des fonctions primitives. Gauthier-Villars, Paris (1928)

    MATH  Google Scholar 

  10. Lebesgue, H.: Measure and the Integral. Holden-Day, San Francisco (1966)

    MATH  Google Scholar 

  11. Natanson, I.P.: Theory of Functions of a Real Variable. Frederick Ungar Publishing Co., New York (1955)

    Google Scholar 

  12. Riesz, F., Sz.-Nagy, B.: Functional Analysis. Dover, New York (1990)

    Google Scholar 

  13. Tao, T.: Analysis I. Hindustan Book Academy, New Delhi, India (2009)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Ovchinnikov, S. (2013). Lebesgue Measure. In: Measure, Integral, Derivative. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7196-7_2

Download citation

Publish with us

Policies and ethics