▁and ▁the ▁stability ▁of ▁these ▁definitions ▁under ▁different ▁models ▁of ▁computation , ▁give ▁evidence ▁that ▁Martin - L ö f ▁random ness ▁is ▁a ▁fundamental ▁property ▁of ▁mathematics ▁and ▁not ▁an ▁accident ▁of ▁Martin - L ö f ' s ▁particular ▁model . ▁The ▁th esis ▁that ▁the ▁definition ▁of ▁Martin - L ö f ▁random ness ▁" correct ly " ▁capt ures ▁the ▁intuit ive ▁notion ▁of ▁random ness ▁has ▁been ▁called ▁the ▁Martin - L ö f – Ch ait in ▁Th esis ; ▁it ▁is ▁somewhat ▁similar ▁to ▁the ▁Church – T uring ▁th esis . ▁ ▁Three ▁equivalent ▁definitions ▁▁ ▁Martin - L ö f ' s ▁original ▁definition ▁of ▁a ▁random ▁sequence ▁was ▁in ▁terms ▁of ▁construct ive ▁null ▁covers ; ▁he ▁defined ▁a ▁sequence ▁to ▁be ▁random ▁if ▁it ▁is ▁not ▁contained ▁in ▁any ▁such ▁cover . ▁ ▁Leon id ▁Le vin ▁and ▁Cla us - Peter ▁Sch nor r ▁proved ▁a ▁character ization ▁in ▁terms ▁of ▁algorithm ic ▁complexity : ▁ ▁a ▁sequence ▁is ▁random ▁if ▁there ▁is ▁a ▁uniform ▁bound ▁on ▁the ▁compress ibility ▁of ▁its ▁initial ▁segments . ▁▁ ▁Sch nor r ▁gave ▁a ▁third ▁equivalent ▁definition ▁in ▁terms ▁of ▁mart ing ales . ▁ ▁Li ▁and ▁Vit any i ' s ▁book ▁An ▁Introduction ▁to ▁Kol m og or ov ▁Complex ity ▁and ▁Its ▁App lications ▁is ▁the ▁standard ▁introduction ▁to ▁these ▁ideas . ▁▁ ▁Algorithm ic ▁complexity ▁( S chn orr ▁ 1 9 7 3 , ▁Le vin ▁ 1 9