Skip to main content
SpringerLink
Log in

Preliminaries

  • Chapter
  • First Online:
Measure, Integral, Derivative

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

  • 4931 Accesses

Abstract

Real analysis is a standard prerequisite for a course on Lebesgue’s theories of measure, integration, and derivative. The goal of this chapter is to bring readers with different backgrounds in real analysis to a common starting point. In no way the material here is a substitute for a systematic course in real analysis. Our intention is to fill the gaps between what some readers may have learned before and what is required to fully understand the material presented in the consequent chapters.

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 16.99
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

  1. Department of Mathematics, San Francisco State University, San Francisco, CA, USA

    Sergei Ovchinnikov

Authors
  1. Sergei Ovchinnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Ovchinnikov, S. (2013). Preliminaries. In: Measure, Integral, Derivative. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7196-7_1

Download citation

Publish with us

Policies and ethics

Search

Navigation