For the study of relevant definitions and theorems of fuzzy integrals

a fuzzy measure is first defined; then a pair of optimized Einstein operators of the form are designed

which are λ-fuzzy quasiproduct operator and λ-fuzzy quasisum operator respectively. It is proved that the T triangular norm and S triangular norm conditions are satisfied. Finally

the definition of λ-fuzzy product probability integral and its theorem are given on the η-fuzzy measure space

and the proof of the theorem is also given

thus enriching the content of fuzzy measure theory.