Consider three normal operators A,B,C on a separable Hilbert space ? as well scalar-valued spectral measures ? A ?(A), B ?(B) and C ?(C). For any ??L ? (? ×? ) X,Y?S 2 (?), the of Hilbert–Schmidt ?, we provide general definition triple operator integral ? (?)(X,Y) belonging to S (?) in such way that (?) belongs (S (?)×S (?),S (?)) bounded bilinear resulting mapping :L )?B is w * -continuous iso...