▁containing ▁its ▁center ▁point : ▁ ▁The ▁nest ing ▁ax iom ▁impos es ▁the ▁property ▁of ▁" cl ust ering " ▁which ▁is ▁characteristic ▁of ▁info - g ap ▁uncertainty . ▁Furthermore , ▁the ▁nest ing ▁ax iom ▁implies ▁that ▁the ▁uncertainty ▁sets ▁ ▁become ▁more ▁inclus ive ▁as ▁ ▁grows , ▁thus ▁end ow ing ▁ ▁with ▁its ▁meaning ▁as ▁a ▁horizon ▁of ▁uncertainty . ▁The ▁contra ction ▁ax iom ▁implies ▁that , ▁at ▁horizon ▁of ▁uncertainty ▁zero , ▁the ▁estimate ▁ ▁is ▁correct . ▁ ▁Rec all ▁that ▁the ▁uncertain ▁element ▁ ▁may ▁be ▁a ▁parameter , ▁vector , ▁function ▁or ▁set . ▁The ▁info - g ap ▁model ▁is ▁then ▁an ▁un bounded ▁family ▁of ▁nested ▁sets ▁of ▁parameters , ▁vectors , ▁functions ▁or ▁sets . ▁ ▁Sub level ▁sets ▁ ▁For ▁a ▁fixed ▁point ▁estimate ▁ ▁an ▁info - g ap ▁model ▁is ▁often ▁equivalent ▁to ▁a ▁function ▁ ▁defined ▁as : ▁ ▁meaning ▁" the ▁uncertainty ▁of ▁a ▁point ▁u ▁is ▁the ▁minimum ▁uncertainty ▁such ▁that ▁u ▁is ▁in ▁the ▁set ▁with ▁that ▁uncertainty ". ▁In ▁this ▁case , ▁the ▁family ▁of ▁sets ▁ ▁can ▁be ▁recovered ▁as ▁the ▁sub level ▁sets ▁of ▁: ▁ ▁meaning : ▁" the ▁nested ▁subset ▁with ▁horizon ▁of ▁uncertainty ▁ ▁consists ▁of ▁all ▁points ▁with ▁uncertainty ▁less ▁than ▁or ▁equal ▁to ▁". ▁ ▁Con vers ely , ▁given ▁a ▁function ▁ ▁satisfying ▁the ▁ax iom ▁ ▁( equ ival ently , ▁ ▁if ▁and ▁only ▁if ▁), ▁it ▁defines ▁an ▁info -