17/12/16 14:38:16.03 /2xvBEHK.net
>>112 つづき
[17] Alec Norton [Kercheval], "Continued fractions and differentiability of functions", American Mathematical Monthly 95 #7 (Aug./Sept. 1988), 639-643. [MR 89j:26009; Zbl 654.26006]
On p. 643, Norton proves the following result.
THEOREM:
Let f:R --> R be discontinuous on a set of points that is dense in R.
Then there exists a co-meager (i.e. residual) set B such that for all x in B and for all s > 0, f fails to satisfy a pointwise Holder condition of order (exponent) s at x.
NOTE: See also the comments I make in Heuer [15] and Nymann [16] above.
(引用終り)
以上