18/10/18 11:49:15.20 iaTtGtuu.net
>>369
>(Each co-meager set has c points in every interval.）”
>と同じ程度のボリュームの証明になるだろうと分っているんじゃないかな？（＾＾；
＜前振り開始＞
（>>252より再録）
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Topic: Differentiability of the Ruler Function
The Math Forum
Dave L. Renfro Registered: 12/3/04
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Differentiability of the Ruler Function
Posted: Dec 13, 2006 5:20 PM
The ruler function f is defined by f(x) = 0 if x is
irrational, f(0) = 1, and f(x) = 1/q if x = p/q
where p and q are relatively prime integers with q > 0.
Here is a summary of the main results below.
In this summary, f always refers to the ruler
function as defined above.
** f is nowhere differentiable.
We would expect higher powers of f to be smoother,
and this is what we find. Note that for each r > 0,
the sets where f^r is continuous and discontinuous
is the same as for f.
（注：つまりf^r(x) = (1/q)^r if x = p/q）
** For each 0 < r <= 2, f^r is nowhere differentiable.
** For each r > 2, f^r is differentiable on a set that
has c many points in every interval.
つづく