@MISC{INTEGR24.MIZ,
  AUTHOR = {Endou, Noboru},
  TITLE = {Improper Integral, Part {I}},
  DAY = {30},
  MONTH = {September},
  YEAR = {2021},
  ADDRESS1 = {National Institute of Technology, Gifu College\\2236-2 Kamimakuwa, Motosu, Gifu, Japan},
  SECTION1 = {Preliminaries},
  SECTION2 = {Properties of Extended Riemann Integral},
  SECTION3 = {Definition of Improper Integral},
  SECTION4 = {Linearity of Improper Integral},
  SUMMARY = {In this article, we deal with Riemann's improper integral. Improper 
    integrals with finite values are discussed in INTEGR10 \cite{INTEGR10.abs} by 
    Yamazaki et al., but in general, improper integrals do not assume that they 
    are finite. Therefore, we have formalized general improper integrals that does 
    not limit the integral value to a finite value. In addition, each theorem of 
    INTEGR10 assumes that the domain of integrand includes a closed
   interval, but since the improper integral should be discusses based on 
   the half-open interval, we also corrected it.}}