@MISC{INTEGR20.MIZ,
  AUTHOR = {Narita, Keiko and Endou, Noboru and Shidama, Yasunari},
  TITLE = {Riemann Integral of Functions from $\mathbbbR$ into Real {B}anach Space},
  ACKNOWLEDGEMENT = {This work was supported by
    JSPS KAKENHI 22300285, 23500029.},
  SECTION1 = {Some Properties of Continuous Functions},
  SECTION2 = {Some Properties of Sequences},
  DAY = {18},
  MONTH = {June},
  YEAR = {2013},
  ADDRESS1 = {Hirosaki-city, Aomori, Japan},
  ADDRESS2 = {Gifu National College of Technology, Gifu, Japan},
  ADDRESS3 = {Shinshu University\\Nagano},
  SUMMARY = {In this article, we deal with the Riemann integral
  of functions from $\mathbbbR$ into a real Banach space.
  The last theorem establishes the integrability of continuous
  functions on the closed interval of reals.
  To prove the integrability, we defined uniform
  continuity for functions from
  $\mathbbbR$ into a real normed space and proved related theorems.
  We also stated some properties of finite
  sequences of elements of a real normed space and
  finite sequences of real numbers.\par
  In addition, we proved some theorems about the convergence of sequences.
  We applied definitions introduced in
  the previous article \cite{INTEGR18.ABS} to
  the proof of integrability.}}



