g ap ▁model ▁via ▁the ▁sub level ▁sets . ▁ ▁For ▁instance , ▁if ▁the ▁region ▁of ▁uncertainty ▁is ▁a ▁metric ▁space , ▁then ▁the ▁uncertainty ▁function ▁can ▁simply ▁be ▁the ▁distance , ▁ ▁so ▁the ▁nested ▁subsets ▁are ▁simply ▁ ▁This ▁always ▁defines ▁an ▁info - g ap ▁model , ▁as ▁distances ▁are ▁always ▁non - negative ▁( ax iom ▁of ▁non - neg ativity ), ▁and ▁satisfies ▁ ▁( info - g ap ▁ax iom ▁of ▁contra ction ) ▁because ▁the ▁distance ▁between ▁two ▁points ▁is ▁zero ▁if ▁and ▁only ▁if ▁they ▁are ▁equal ▁( the ▁identity ▁of ▁ind isc ern ibles ); ▁nest ing ▁follows ▁by ▁construction ▁of ▁sub level ▁set . ▁ ▁Not ▁all ▁info - g ap ▁models ▁arise ▁as ▁sub level ▁sets : ▁for ▁instance , ▁if ▁ ▁for ▁all ▁ ▁but ▁not ▁for ▁ ▁( it ▁has ▁uncertainty ▁" just ▁more " ▁than ▁ 1 ), ▁then ▁the ▁minimum ▁above ▁is ▁not ▁defined ; ▁one ▁can ▁replace ▁it ▁by ▁an ▁inf imum , ▁but ▁then ▁the ▁resulting ▁sub level ▁sets ▁will ▁not ▁agree ▁with ▁the ▁inf og ap ▁model : ▁ ▁but ▁ ▁The ▁effect ▁of ▁this ▁distinction ▁is ▁very ▁minor , ▁however , ▁as ▁it ▁mod ifies ▁sets ▁by ▁less ▁than ▁changing ▁the ▁horizon ▁of ▁uncertainty ▁by ▁any ▁positive ▁number ▁ ▁however ▁small . ▁ ▁Rob ust ness ▁and ▁opportun eness ▁ ▁Un certain ty ▁may ▁be ▁either ▁per n icious ▁or ▁prop it ious . ▁That ▁is , ▁uncertain ▁variations ▁may ▁be ▁either ▁ad