Firstly,　we　obtain　sample　path　large　deviations　for　compact　random　sets,　the　main　tool　is　a　result　of　large　deviations　on　D([0,　1],　B)　with　the　uniform　metric.　We　also　show　that　Cerf＇s　result　(1999)　[5]　is　only　a　corollary　of　sample　path　large　deviations.　Secondly,　we　obtain　large　deviations　and　moderate　deviations　of　random　sets　which　take　values　of　bounded　closed　convex　sets　on　the　underling　separable　Banach　space　with　respect　to　the　Hausdorff　distance　d(H)　and　that　of　random　upper　semicontinuous　functions　whose　values　are　of　bounded　closed　convex　levels　on　the　underling　separable　Banach　space　in　the　sense　of　the　uniform　Hausdorff　distance　d(H)(infinity).　The　main　tool　is　the　work　of　Wu　on　the　large　deviations　and　moderate　deviations　for　empirical　processes　(Wu,　1994)　[21].　Finally,　we　prove　that　Lemma　2　in　[5],　which　is　very　important　for　＂deconvexification＂,　still　holds　under　another　condition　E[exp{lambda　parallel　to　X　parallel　to(p)(K)}]　＜　infinity　for　some　lambda　＞　0　in　a　different　proof　method.　(C)　2012　Elsevier　Inc.　All　rights　reserved.