Holder's enequality refers to the folowing elementary, though foundamental, inequality between the maduli of any pair set complex numbers ?,??C ( k=?,…,n) : (?|?_k ?_k |^r )^?\\r?(?(|?_k |^p)^?\\p))(?(|?_k |^q)^?\\q)) where p , q , r are positive reale number such that. Horn and Zhan have generated (?) for A , B ? B(H) in the folowing form |||A^*B|||^r |||A|^pr|||^?\\p||||B|^qr|||^?\\q Kittaneh obtained that if A_i , X_i , Y_i ? B(H) ( i=?, ..., n ) r ? , then ||||?X^*A_iX_i|^r|||^? ||||?X^*|A_i^*|X_i)^r||| |||(?Y^*|A_i|)Y_i)^r||| The major aim of this dissertation is to examin new inequality (?) might holds for measurable operators associated with a semi-finite vin Neumann algebra.