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Fubini’s Theorem for Non-Negative or Non-Positive Functions Cover

Fubini’s Theorem for Non-Negative or Non-Positive Functions

By: Noboru Endou  
Open Access
|Jul 2018

References

  1. [1] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.10.1007/978-3-319-20615-8_17
  2. [2] Heinz Bauer. Measure and Integration Theory. Walter de Gruyter Inc., 2002.10.1515/9783110866209
  3. [3] Vladimir Igorevich Bogachev and Maria Aparecida Soares Ruas. Measure theory, volume 1. Springer, 2007.
  4. [4] Noboru Endou. Product pre-measure. Formalized Mathematics, 24(1):69–79, 2016. doi:10.1515/forma-2016-0006.10.1515/forma-2016-0006
  5. [5] Noboru Endou. Fubini’s theorem on measure. Formalized Mathematics, 25(1):1–29, 2017. doi:10.1515/forma-2017-0001.10.1515/forma-2017-0001
  6. [6] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53–70, 2006. doi:10.2478/v10037-006-0008-x.10.2478/v10037-006-0008-x
  7. [7] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491–494, 2001.
  8. [8] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. The measurability of extended real valued functions. Formalized Mathematics, 9(3):525–529, 2001.
  9. [9] Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.10.1007/s10817-015-9345-1
  10. [10] P. R. Halmos. Measure Theory. Springer-Verlag, 1974.
  11. [11] Johannes Hölzl and Armin Heller. Three chapters of measure theory in Isabelle/HOL. In Marko C. J. D. van Eekelen, Herman Geuvers, Julien Schmaltz, and Freek Wiedijk, editors, Interactive Theorem Proving (ITP 2011), volume 6898 of LNCS, pages 135–151, 2011.10.1007/978-3-642-22863-6_12
  12. [12] Yasushige Watase, Noboru Endou, and Yasunari Shidama. On L1 space formed by real-valued partial functions. Formalized Mathematics, 16(4):361–369, 2008. doi:10.2478/v10037-008-0044-9.10.2478/v10037-008-0044-9
DOI: https://doi.org/10.2478/forma-2018-0005 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 49 - 67
Submitted on: Mar 27, 2018
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Published on: Jul 28, 2018
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2018 Noboru Endou, published by University of Białystok
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.