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This is just a reference request. I thought I'd come across a paper demonstrating that there is a translation invariant measure on an infinite-dimensional space without 'points' whilst browsing the net a few days ago. But I can't seem to find the link.

Has such a thing been demonstrated?

I've linked it in with toposes & locales as those are the spaces I know of without points.

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  • $\begingroup$ What is a space without points? $\endgroup$
    – user1688
    Commented Jul 22, 2013 at 14:42
  • $\begingroup$ When someone refers to point-free topology or spaces without points, they are referring to frames and locales. Also, frames and locales are pretty much the same thing. The only difference between frames and locales is that the morphisms in the category of locales go the opposite direction. See the book Frames and Locales- Topology Without Points for more details. $\endgroup$
    – Joseph Van Name
    Commented Jul 22, 2013 at 16:51
  • $\begingroup$ On the other hand, while presumably the question isn't so urgent since no clarification has been forthcoming, it could be that the measure, not the space, is meant to be without 'points'—in which case it could be that what is meant is a non-atomic measure. $\endgroup$
    – LSpice
    Commented Dec 14, 2015 at 23:18

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