@MISC{MESFUN17.MIZ,
  AUTHOR = {Endou, Noboru and Shidama, Yasunari},
  TITLE = {Integral of Continuous Three Variable Functions},
  DAY = {18},
  MONTH = {June},
  YEAR = {2024},
  ADDRESS1 = {National Institute of Technology, Gifu College\\2236-2 Kamimakuwa, Motosu, Gifu, Japan},
  ADDRESS2 = {Karuizawa Hotch 244-1 Nagano, Japan},
  SECTION1 = {Preliminaries},
  SECTION2 = {Properties on the projective function of a three-variable function},
  SECTION3 = {Integral of continuous three-variable functions},
  SUMMARY = {In this article, following the previous article \cite{MESFUN16.ABS}, we continue our proofs on integrals of continuous functions of three variables.
  In the first section, continuity of functions of three variables is shown. These are used in the proofs of the later sections.
  The second section summarizes the basic properties of the projection of a continuous function in three variables, a result that is almost as obvious as in two variables, but is used to transform \cite{MESFUN14.ABS} Riemann and Lebesgue integrals for real-valued functions (not extended real-valued functions).
  In the last section, we prove integrability and iterated integrals of continuous functions of three variables.
  Throughout the paper, the basic operations follow \cite{Apostol:1967II}, \cite{Edward1958}, and \cite{Serge2012}.},
  ACKNOWLEDGEMENT = {This work was supported by JSPS KAKENHI 23K11242.}}
  