17/12/09 15:27:35.83 OrUOLzdR.net
>>442 追加
重複を厭わず、下記追加引用
（下記より）
”THEOREM: Let g be continuous and discontinuous on sets
of points that are each dense in the reals.
Then g fails to have a derivative on a
co-meager (residual) set of points. In fact,
g fails to satisfy a pointwise Lipschitz
condition, a pointwise Holder condition,
or even any specified pointwise modulus of
continuity condition on a co-meager set.”
ここで、”Let g be continuous and discontinuous on sets of points that are each dense in the reals.”
とあるでしょ。この”each dense in the reals”を覚えておいてね。あとで使う（＾＾
（>>285より）
URLﾘﾝｸ(mathforum.org)
Topic: Differentiability of the Ruler Function Dave L. Renfro Posted: Dec 13, 2006 Replies: 3 Last Post: Jan 10, 2007
(抜粋)
** f_w is differentiable on a set whose complement
has Hausdorff dimension zero. Jurek [4] (pp. 24-25)
Interesting, each of the sets of points where these
functions fail to be differentiable is large in the
sense of Baire category.
THEOREM: Let g be continuous and discontinuous on sets
of points that are each dense in the reals.
Then g fails to have a derivative on a
co-meager (residual) set of points. In fact,
g fails to satisfy a pointwise Lipschitz
condition, a pointwise Holder condition,
or even any specified pointwise modulus of
continuity condition on a co-meager set.
(Each co-meager set has c points in every interval.)
There are 22 items below. I found 4 of them on the internet,
I provide the complete text for 9 of them, and I give
some idea of what the remaining 9 items involve.
On the internet -- [2], [4], [11], [22].
Text provided below -- [1], [3], [5], [6], [12], [13],
[14], [19], [21].
(引用終り)