Skip to main content
SpringerLink
Log in

On Lusin’s Theorem for Non-additive Measure

  • Conference paper
Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

  • 1855 Accesses

Abstract

In this paper, we prove Lusin’s theorem remains valid for nonadditive Borel measure under the conditions of weakly null additivity, continuity from above and a certain additional continuity.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Denneberg, D.: Non-Additive Measure and Integral, 2nd edn. Kluwer Academic Publishers, Dordrecht (1997)

    Google Scholar 

  2. Jiang, Q., Suzuki, H.: Fuzzy measures on metric spaces. Fuzzy Sets and Systems 83, 99–106 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Jiang, Q., Wang, S., Ziou, D.: A further investigation for fuzzy measures on metric spaces. Fuzzy Sets and Systems 105, 293–297 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kawabe, J.: Regularity and Lusin’s theorem for Riesz space-valued fuzzy measures. Fuzzy Sets and Systems 158, 895–903 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Li, J., Yasuda, M.: Lusin’s theorems on fuzzy measure spaces. Fuzzy Sets and Systems 146, 121–133 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Li, J., Yasuda, M., Jiang, Q., Suzuki, H., Wang, Z., Klir, G.J.: Convergence of sequence of measurable functions on fuzzy measure spaces. Fuzzy Sets and Systems 87, 317–323 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Pap, E.: Null-Additive Set Functions. Kluwer Academic Publishers, Dordrecht (1995)

    Google Scholar 

  8. Royden, H.L.: Real Analysis. Macmillan, New York (1966)

    Google Scholar 

  9. Song, J., Li, J.: Regularity of null-additive fuzzy measure on metric spaces. International Journal of General Systems 32, 271–279 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Sun, Q.: Property (S) of fuzzy measure and Riesz’s theorem. Fuzzy Sets and Systems 62, 117–119 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang, Z., Klir, G.J.: Fuzzy Measure Theory. Plenum Press, New York (1992)

    MATH  Google Scholar 

  12. Watanabe, T., Tanaka, T.: On regularity for non-additive measure (preprint)

    Google Scholar 

  13. Wu, C., Ha, M.: On the regularity of the fuzzy measure on metric fuzzy measure spaces. Fuzzy Sets and Systems 66, 373–379 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wu, J., Wu, C.: Fuzzy regular measures on topological spaces. Fuzzy Sets and Systems 119, 529–533 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Science and Technology, Niigata University, 8050, Ikarashi 2-no-cho, Nishi-ku, Niigata, 950–2181, Japan

    Tamaki Tanaka & Toshikazu Watanabe

Authors
  1. Tamaki Tanaka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Toshikazu Watanabe
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tanaka, T., Watanabe, T. (2011). On Lusin’s Theorem for Non-additive Measure. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22833-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation