@MISC{INTEGR16.MIZ,
  AUTHOR = {Miyajima, Keiichi and Kato, Takahiro and Shidama, Yasunari},
  TITLE = {Riemann Integral of Functions $\mathbbbR$ into $\mathbbbC$},
  ACKNOWLEDGEMENT = {I would like to express my gratitude to
    Prof. Yatsuka Nakamura.},
  SECTION1 = {Preliminaries},
  SECTION2 = {Definition of Riemann Integral on
    Functions $\mathbbbR$ into $\mathbbbC$},
  SECTION3 = {Linearity of the Integration Operator},
  DAY = {23},
  MONTH = {February},
  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
  $\mathbbbR$ into $\mathbbbC$ and proof the linearity of this operator.
  Especially, the Riemann integral of complex functions is constituted
  by the redefinition about the Riemann sum of complex numbers.
  Our method refers to the \cite{Murray:1974}.}}

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