Re: [HM] Cantor on the Cantor set?
William Tait (wtait@ix.netcom.com)
Sun, 10 Jan 1999 13:03:11 -0600
David Fowler (12:50 AM 1/10/99) wrote
>>> Can someone inform me about the accurate historical date and place,
>>> when and where did...
>
>Since we're on this kind of thing, can I also ask about the Cantor set?
>
>My feeling, based on no reliable knowledge, is that it is in a footnote in
>??, where he refers to it in a rather offhand kind of way, as if it was a
>well-known construction.
The construction is in ``\"Uber unendliche lineare
Punktmannigfaltigkeiten'', Number 4.
>On the other hand, a variant of it, a non-closed 'end nth' rather than a
>closed 'middle third' set, was given in:
>
>HJS Smith, On the integration of discontinuous functions, Proceedings of
>the London Math Soc 6 (1875) 140-153.
In Thomas Hawkins' *Lebesgue's Theory of Integration*, pp. 37-41, there is
a discussion of Smith's work.
Bill