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

[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_17Open DOISearch in Google Scholar

[2] Heinz Bauer. Measure and Integration Theory. Walter de Gruyter Inc., 2002.10.1515/9783110866209Search in Google Scholar

[3] Vladimir Igorevich Bogachev and Maria Aparecida Soares Ruas. Measure theory, volume 1. Springer, 2007.Search in Google Scholar

[4] Noboru Endou. Product pre-measure. Formalized Mathematics, 24(1):69–79, 2016. doi:10.1515/forma-2016-0006.10.1515/forma-2016-0006Open DOISearch in Google Scholar

[5] Noboru Endou. Fubini’s theorem on measure. Formalized Mathematics, 25(1):1–29, 2017. doi:10.1515/forma-2017-0001.10.1515/forma-2017-0001Open DOISearch in Google Scholar

[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-xOpen DOISearch in Google Scholar

[7] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Basic properties of extended real numbers. Formalized Mathematics, 9(3):491–494, 2001.Search in Google Scholar

[8] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. The measurability of extended real valued functions. Formalized Mathematics, 9(3):525–529, 2001.Search in Google Scholar

[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/s10817-015-9345-1Open DOISearch in Google Scholar

[10] P. R. Halmos. Measure Theory. Springer-Verlag, 1974.Search in Google Scholar

[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_12Search in Google Scholar

[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/v10037-008-0044-9Open DOISearch in Google Scholar