The extension of a *-isomorphism between two real W*-algebras to a *-isomorphism of the corresponding *-algebras of all m-measurable operators

The subadditive measures (denoted by m) on projectors of the real von Neumann algebra are
considered. A theorem on the extension of a *-isomorphism between two real von Neumann algebras
to a *-isomorphism of the corresponding *-algebras of all m-measurable operators has been proved.