@MISC{INTEGR18.MIZ,
  AUTHOR = {Miyajima, Keiichi and Kato, Takahiro and Shidama, Yasunari},
  TITLE = {Riemann Integral of Functions from $\mathbbbR$
     into Real Normed Space},
  ACKNOWLEDGEMENT = {We would like to express my
    gratitude to Prof. Yatsuka Nakamura.},
  SECTION1 = {Preliminaries},
  SECTION2 = {Definition of Riemann Integral on Functions
    from $\mathbbbR$ into Real Normed Space},
  SECTION3 = {Linearity of the Integration Operator},
  DAY = {20},
  MONTH = {May},
  YEAR = {2010},
  ADDRESS1 = {Ibaraki University, Faculty of Engineering, Hitachi\\ Ibaraki},
  ADDRESS2 = {Graduate School of Ibaraki University, Faculty of Engineering\\ Hitachi, Ibaraki},
  ADDRESS3 = {Shinshu University\\ Nagano},
  SUMMARY={In this article, we define the Riemann integral on functions from
  $\mathbbbR$ into real normed space and prove the linearity of
  this operator.
  As a result, the Riemann integration can be applied to a wider
  range of functions. The proof method follows the \cite{Murray:1974}.}}

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