@MISC{INTEGR21.MIZ,
  AUTHOR = {Narita, Keiko and Endou, Noboru and Shidama, Yasunari},
  TITLE = {The Linearity of Riemann Integral on Functions
   from $\mathbbbR$ into Real {B}anach Space},
  ACKNOWLEDGEMENT = {This work was supported by JSPS KAKENHI 22300285,
     23500029.},
  SECTION1 = {Some Properties of Bounded Functions},
  SECTION2 = {Some Properties of Integral of Continuous Functions},
  DAY = {7},
  MONTH = {October},
  YEAR = {2013},
  ADDRESS1 = {Hirosaki-city, Aomori, Japan},
  ADDRESS2 = {Gifu National College of Technology, Gifu, Japan},
  ADDRESS3 = {Shinshu University\\Nagano},
  SUMMARY = {In this article, we described basic properties
  of Riemann integral on functions from $\mathbbbR$ into Real Banach space.
   We proved mainly the linearity of integral operator about
   the integral of continuous functions on closed interval of the set of real
   numbers.
   These theorems were based on the article \cite{INTEGR19.ABS}
   and we referred to the former articles about Riemann integral.
   We applied definitions and theorems introduced in
   the article \cite{INTEGR18.ABS} and the article
   \cite{INTEGR20.ABS} to the proof.
   Using the definition of the article \cite{INTEGR19.ABS},
   we also proved some theorems on bounded functions.}}

