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SUMMARY:Linda Brown Westrick (Penn State)
DTSTART:20201208T210000Z
DTEND:20201208T220000Z
DTSTAMP:20260423T005738Z
UID:CTA/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CTA/29/">Luz
 in's (N) and randomness reflection</a>\nby Linda Brown Westrick (Penn Stat
 e) as part of Computability theory and applications\n\n\nAbstract\nWe show
  that a computable real-valued function f has Luzin's property (N) if and 
 only if it reflects Pi^1_1-randomness\, if and only if it reflects Delta^1
 _1-randomness relative to Kleene's O\, and if and only if it reflects Kurt
 z randomness relative to Kleene's O.  Here a function f is said to reflect
  a randomness notion R if whenever f(x) is R-random\, then x is R-random a
 s well. If additionally f is known to have bounded variation\, then we sho
 w f has Luzin's (N) if and only if it reflects weak-2-randomness\, and if 
 and only if it reflects Kurtz randomness relative to 0'.  This links class
 ical real analysis with algorithmic randomness.  Joint with Arno Pauly and
  Liang Yu.\n
LOCATION:https://researchseminars.org/talk/CTA/29/
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