We　establish　in　this　paper　a　priori　global　W-2,W-delta　estimates　for　singular　fully　nonlinear　elliptic　equations　with　L-n　right　hand　side　terms.　The　method　is　to　slide　paraboloids　and　barrier　functions　vertically　to　touch　the　solution　of　the　equation,　and　then　to　estimate　the　measure　of　the　contact　set　in　terms　of　the　measure　of　the　vertex　point　set.　To　derive　global　estimates　from　L-n　data,　the　Hardy-Littlewood　maximal　functions,　appropriate　localizations　and　a　new　type　of　covering　argument　are　adopted.　These　methods　also　provide　us　a　more　direct　proof　of　the　W-2,W-delta　estimates　for　(nonsingular)　fully　nonlinear　elliptic　equations　established　by　L.　A.　Caffarelli　and　X.　Cabre.　(C)　2018　Elsevier　Ltd.　All　rights　reserved.