@MISC{INTEGR19.MIZ,
  AUTHOR = {Miyajima, Keiichi and Korni{\l}owicz, Artur and Shidama, Yasunari},
  TITLE = {Riemann Integral of Functions from $\mathbbbR$ into
    $n$-dimensional Real Normed Space},
  ACKNOWLEDGEMENT = {We would like to express our
    gratitude to Prof. Yatsuka Nakamura.
  This work was supported by JSPS KAKENHI 22300285.},
  SECTION1 = {On the Functions from $\mathbbbR$ into
    $n$-dimensional Real Space},
  SECTION2 = {On the Functions from $\mathbbbR$ into $n$-dimensional
    Real Normed Space},
  SECTION3 = {Fundamental Theorem of Calculus},
  DAY = {27},
  MONTH = {October},
  YEAR = {2011},
  ADDRESS1 = {Ibaraki University, Faculty of Engineering, Hitachi,\\Ibaraki, Japan},
  ADDRESS2 = {University of Bia{\l}ystok, Institute of Informatics,\\Bia{\l}ystok, Poland},
  ADDRESS3 = {Shinshu University\\Nagano, Japan},
  SUMMARY = {In this article, we define the Riemann integral on functions
  $\mathbbbR$ into $n$-dimensional real normed space and prove the linearity
   of this operator.
  As a result, the Riemann integration can be applied to the wider range.
  Our method refers to the \cite{Murray:1974}.}}

@BOOK{Murray:1974,
 AUTHOR={Spiegel, Murray R.},
 TITLE={Theory and Problems of Vector Analysis},
 PUBLISHER={McGraw-Hill},
 YEAR=1974}

