Lipschitz functions with unexpectedly large sets of nondifferentiability points
2005 ◽
Vol 2005
(4)
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pp. 361-373
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Keyword(s):
It is known that everyGδsubsetEof the plane containing a dense set of lines, even if it has measure zero, has the property that every real-valued Lipschitz function onℝ2has a point of differentiability inE. Here we show that the set of points of differentiability of Lipschitz functions inside such sets may be surprisingly tiny: we construct aGδsetE⊂ℝ2containing a dense set of lines for which there is a pair of real-valued Lipschitz functions onℝ2having no common point of differentiability inE, and there is a real-valued Lipschitz function onℝ2whose set of points of differentiability inEis uniformly purely unrectifiable.
2008 ◽
Vol 8
(1)
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pp. 99-177
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Keyword(s):
2018 ◽
Vol 2020
(21)
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pp. 7433-7453
1957 ◽
Vol 53
(2)
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pp. 312-317
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Keyword(s):
1989 ◽
Vol 39
(2)
◽
pp. 233-238
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Keyword(s):
1993 ◽
Vol 47
(2)
◽
pp. 205-212
◽
1963 ◽
Vol 3
(2)
◽
pp. 134-150
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Keyword(s):