The purpose of this chapter is to present a measurable version of the spectral decomposition theorem for flows. In Sect. 9.1, we introduce another type of expansive measure (called a geometric expansive measure) for flows on a compact metric space. This notion is used to characterize the geometric expansiveness for flows. In Sect. 9.2, we introduce the notion of invariant measure geometric expansive, and prove an extension theorem for invariant measure geometric expansive flows on its chain recurrent set. In Sect. 9.3, we present a measurable version of spectral decomposition theorem which says that if a flow \(\phi \) is invariant measure 1-expansive and shadowing on its chain recurrent set \(CR(\phi )\) then the flow \(\phi \) admits the spectral decomposition.