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SUMMARY:Normality and Differentiability - Heiber\, P A (Universidad de Bue
 nos Aires)
DTSTART:20120705T110000Z
DTEND:20120705T113000Z
UID:TALK38872@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:By transferring to the world of functions computable by finite
  automata the classical theorem of numerical analysis establishing that ev
 ery non-decreasing real valued function is almost everywhere differentiabl
 e\, we obtain a characterization of the property of Borel normality. We co
 nsider functions mapping infinite sequences to infinite sequences and a no
 tion of differentiability that\, on the class of non-decreasing real value
 d functions\, coincides with standard differentiability. We prove that the
  following are equivalent\, for a real x in [0\,1]:\n\n(1) x is normal to 
 base b.\n\n(2) Every non-decreasing function computable by a finite automa
 ton mapping infinite sequences to infinite sequences is differentiable at 
 the expansion of x in base b.\n\n(3) Every non-decreasing function computa
 ble by a finite automaton in base b mapping real numbers to real numbers i
 s differentiable at x.\n\nJoint work with Vernica Becher\, Universidad de 
 Buenos Aires.\n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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