>>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）
https://ja.wikipedia.org/wiki/%E3%83%87%E3%82%A3%E3%83%AA%E3%82%AF%E3%83%AC%E3%81%AE%E9%96%A2%E6%95%B0
ディリクレの関数
(抜粋)
式から分かるように、この関数はいたるところで不連続である。
https://ja.wikipedia.org/wiki/%E3%83%88%E3%83%9E%E3%82%A8%E9%96%A2%E6%95%B0
トマエ関数
(抜粋)
この関数はディリクレの関数を修正したものである。

http://mathforum.org/kb/message.jspa?messageID=5432910
Topic: Differentiability of the Ruler Function
The Math Forum
Dave L. Renfro Registered: 12/3/04
(抜粋)
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