Extension of the structure theorem of Borchers and its application to   half-sided modular inclusions
  A result of H.-W. Wiesbrock is extended from the case of a common cyclic and separating vector for the half-sided modular inclusion of von Neumann algebras to the case of a common faithful normal semifinite weight and at the same time a gap in Wiesbrock's proof is filled in. 
H. Araki, L. Zsido