The Extensions of Egoroff's Theorem and Lusin's Theorem In Operator valued Measure Theory

Abstract

Let $\Omega$ be a measurable space and $\BH$ be the set of all bounded linear operators on the Hilbert space $\h$.  Two fundamental theorems in classical measure theory,   Egoroff's Theorem and Lusin's Theorem, are extended for the operator valued measurable functions $f:\Omega\to\BH$.