f ▁ 1 9 6 6 ): ▁This ▁is ▁Martin - L ö f ' s ▁original ▁definition . ▁For ▁a ▁finite ▁binary ▁string ▁w ▁we ▁let ▁C w ▁denote ▁the ▁cyl inder ▁generated ▁by ▁w . ▁This ▁is ▁the ▁set ▁of ▁all ▁infinite ▁sequences ▁beginning ▁with ▁w , ▁ ▁which ▁is ▁a ▁basic ▁open ▁set ▁in ▁Cant or ▁space . ▁ ▁The ▁product ▁measure ▁▁ μ ( C w ) ▁of ▁the ▁cyl inder ▁generated ▁by ▁w ▁is ▁defined ▁to ▁be ▁▁ 2 − | w | . ▁ ▁Every ▁open ▁subset ▁of ▁Cant or ▁space ▁is ▁the ▁union ▁of ▁a ▁count able ▁sequence ▁of ▁dis joint ▁basic ▁open ▁sets , ▁and ▁the ▁measure ▁of ▁an ▁open ▁set ▁is ▁the ▁sum ▁of ▁the ▁measures ▁of ▁any ▁such ▁sequence . ▁ ▁An ▁effective ▁open ▁set ▁is ▁an ▁open ▁set ▁that ▁is ▁the ▁union ▁of ▁the ▁sequence ▁of ▁basic ▁open ▁sets ▁determined ▁by ▁a ▁recurs ively ▁enumer able ▁sequence ▁of ▁binary ▁strings . ▁ ▁A ▁construct ive ▁null ▁cover ▁or ▁effective ▁measure ▁ 0 ▁set ▁is ▁a ▁recurs ively ▁enumer able ▁sequence ▁ ▁of ▁effective ▁open ▁sets ▁such ▁that ▁ ▁and ▁ ▁for ▁each ▁natural ▁number ▁i . ▁ ▁Every ▁effective ▁null ▁cover ▁determ ines ▁a ▁ ▁set ▁of ▁measure ▁ 0 , ▁namely ▁the ▁intersection ▁of ▁the ▁sets ▁. ▁▁ ▁A ▁sequence ▁is ▁defined ▁to ▁be ▁Martin - L ö f ▁random ▁if ▁it ▁is ▁not ▁contained ▁in ▁any ▁ ▁set ▁determined ▁by ▁a ▁construct ive ▁null ▁cover . ▁▁ ▁Con struct ive