@MISC{MEASURE8.MIZ,
  AUTHOR = {Endou, Noboru and Okazaki, Hiroyuki and Shidama, Yasunari},
  TITLE = {{H}opf Extension Theorem of Measure},
  SECTION1 = {The Outer Measure Induced by the Finite Additive Measure},
  SECTION2 = {Hopf Extension Theorem},
  DAY = {07},
  MONTH = {April},
  YEAR = {2009},
  ADDRESS1 = {Gifu National College of Technology\\ Japan},
  ADDRESS2 = {Shinshu University\\ Nagano, Japan},
  ADDRESS3 = {Shinshu University\\ Nagano, Japan},
  SUMMARY = {The authors have presented some articles about 
  Lebesgue type integration theory. In our previous articles 
  \cite{MESFUNC9.ABS, MESFUNC5.ABS, RINFSUP2.ABS}, we assumed that 
  some $\sigma$-additive measure existed and that a function 
  was measurable on that measure. However the existence of 
  such a measure is not trivial. In general, because the 
  construction of a finite additive measure is comparatively 
  easy, to induce a $\sigma$-additive measure a finite additive 
  measure is used. This is known as an E.~Hopf's extension 
  theorem of measure \cite{Halmos74}.}}

