”. ▁ ▁Each ▁measure ▁ 0 ▁set ▁can ▁be ▁thought ▁of ▁as ▁an ▁un common ▁property . ▁ ▁It ▁is ▁not ▁possible ▁for ▁a ▁sequence ▁to ▁lie ▁in ▁no ▁measure ▁ 0 ▁sets , ▁because ▁each ▁one - point ▁set ▁has ▁measure ▁ 0 . ▁ ▁Martin - L ö f ' s ▁idea ▁was ▁to ▁limit ▁the ▁definition ▁to ▁measure ▁ 0 ▁sets ▁that ▁are ▁effectively ▁descri b able ; ▁the ▁definition ▁of ▁an ▁effective ▁null ▁cover ▁determ ines ▁a ▁count able ▁collection ▁of ▁effectively ▁descri b able ▁measure ▁ 0 ▁sets ▁and ▁defines ▁a ▁sequence ▁to ▁be ▁random ▁if ▁it ▁does ▁not ▁lie ▁in ▁any ▁of ▁these ▁particular ▁measure ▁ 0 ▁sets . ▁▁ ▁Since ▁the ▁union ▁of ▁a ▁count able ▁collection ▁of ▁measure ▁ 0 ▁sets ▁has ▁measure ▁ 0 , ▁this ▁definition ▁immediately ▁leads ▁to ▁the ▁theorem ▁that ▁there ▁is ▁a ▁measure ▁ 1 ▁set ▁of ▁random ▁sequences . ▁Note ▁that ▁if ▁we ▁identify ▁the ▁Cant or ▁space ▁of ▁binary ▁sequences ▁with ▁the ▁interval ▁[ 0 , 1 ] ▁of ▁real ▁numbers , ▁the ▁measure ▁on ▁Cant or ▁space ▁agre es ▁with ▁Leb es gue ▁measure . ▁ ▁The ▁mart ing ale ▁character ization ▁con ve ys ▁the ▁intu ition ▁that ▁no ▁effective ▁procedure ▁should ▁be ▁able ▁to ▁make ▁money ▁bet ting ▁against ▁a ▁random ▁sequence . ▁▁ ▁A ▁mart ing ale ▁d ▁is ▁a ▁bet ting ▁strategy . ▁d ▁reads ▁a ▁finite ▁string ▁w ▁and ▁bet s ▁money ▁on ▁the ▁next ▁bit . ▁It ▁bet s ▁some ▁fraction