In　this　paper,　we　shall　firstly　illustrate　why　we　should　introduce　an　It　type　set-valued　stochastic　differential　equation　and　why　we　should　notice　the　almost　everywhere　problem.　Secondly　we　shall　give　a　clear　definition　of　Aumann　type　Lebesgue　integral　and　prove　the　measurability　of　the　Lebesgue　integral　of　set-valued　stochastic　processes　with　respect　to　time　t.　Then　we　shall　present　some　new　properties,　especially　prove　an　important　inequality　of　set-valued　Lebesgue　integrals.　Finally　we　shall　prove　the　existence　and　the　uniqueness　of　a　strong　solution　to　the　It　type　set-valued　stochastic　differential　equation.