In　this　paper,　we　shall　firstly　illustrate　why　we　should　discuss　the　Aumann　type　set-valued　Lebesgue　integral　of　a　set-valued　stochastic　process　with　respect　to　time　t　under　the　condition　that　the　set-valued　stochastic　process　takes　nonempty　compact　subset　of　d-dimensional　Euclidean　space.　After　recalling　some　basic　results　about　set-valued　stochastic　processes,　we　shall　secondly　prove　that　the　Aumann　type　set-valued　Lebesgue　integral　of　a　set-valued　stochastic　process　above　is　a　set-valued　stochastic　process.　Finally　we　shall　give　the　representation　theorem,　and　prove　an　important　inequality　of　the　Aumann　type　set-valued　Lebesgue　integrals　of　set-valued　stochastic　processes　with　respect　to　t,　which　are　useful　to　study　set-valued　stochastic　differential　inclusions　with　applications　in　finance.