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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeJun 4th 2011
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   Author: zskoda
   Format: MarkdownItexNew entries [[operator topology]] (for now redirecting also [[strong operator topology]] etc.) and [[unitary representation]]. Changes at [[projection measure]] (the sigma algebra does not need to be the sigma algebra of Borel subsets on a topological space!) and [[spectral measure]]. At some point one should add some crosslinks from/to other entries in [[functional analysis]] but I am on slow/expensive connection now, hence will restrain to more substantial (in content sense) edits.

   New entries operator topology (for now redirecting also strong operator topology etc.) and unitary representation. Changes at projection measure (the sigma algebra does not need to be the sigma algebra of Borel subsets on a topological space!) and spectral measure. At some point one should add some crosslinks from/to other entries in functional analysis but I am on slow/expensive connection now, hence will restrain to more substantial (in content sense) edits.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeJun 4th 2011
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   Author: zskoda
   Format: MarkdownItexMore in this vein: [[locally compact topological group]], [[system of imprimitivity]], [[Gelfand-Raikov theorem]], [[Radon measure]].

   More in this vein: locally compact topological group, system of imprimitivity, Gelfand-Raikov theorem, Radon measure.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 4th 2011
   • (edited Jun 4th 2011)
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   Author: Urs
   Format: MarkdownItexThanks for all this. I have added a few links here and there. For instance started a list of Example-links at [[measure]]. At some point we should start a subject cluster / floating toc on "measure theory" or the like.

   Thanks for all this. I have added a few links here and there. For instance started a list of Example-links at measure.

   At some point we should start a subject cluster / floating toc on “measure theory” or the like.

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeJun 4th 2011
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   Author: zskoda
   Format: MarkdownItexMy intention was not toward measure theory. I primarily want to create some entries which will help write something about the Tannaka duality theorems for groups in full power, for what one needs much harmonic analysis. Matija will be giving a seminar in few days in Zagreb on this topic.

   My intention was not toward measure theory. I primarily want to create some entries which will help write something about the Tannaka duality theorems for groups in full power, for what one needs much harmonic analysis. Matija will be giving a seminar in few days in Zagreb on this topic.

5. • CommentRowNumber5.
   • CommentAuthorzskoda
   • CommentTimeJun 4th 2011
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   Author: zskoda
   Format: MarkdownItexBy the way, under Tannaka duality, it is currently > for A some __algebraic__ structure, represented on objects in a category D, one may reconstruct A from knowledge of the endomorphisms of the forgetful functor – the fiber functor I will change that: A should be a __symmetry__ object. Typical important examples are far from __algebraic__ in the sense of category theory, better they are locally compact group(oid)s, gerbes and so on. "Algebraic" is I think misleading here (of course, symmetries act so there is something algebraic about it, but any place category theory comes in is algebraic to a similar extent).

   By the way, under Tannaka duality, it is currently

   for A some algebraic structure, represented on objects in a category D, one may reconstruct A from knowledge of the endomorphisms of the forgetful functor – the fiber functor

   I will change that: A should be a symmetry object. Typical important examples are far from algebraic in the sense of category theory, better they are locally compact group(oid)s, gerbes and so on. “Algebraic” is I think misleading here (of course, symmetries act so there is something algebraic about it, but any place category theory comes in is algebraic to a similar extent).

6. • CommentRowNumber6.
   • CommentAuthorDavid_Corfield
   • CommentTimeFeb 8th 2012
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   Author: David_Corfield
   Format: MarkdownItexZoran #1 >the sigma algebra does not need to be the sigma algebra of Borel subsets on a topological space! Does this mean you can answer this [MO question](http://mathoverflow.net/questions/87838/is-every-sigma-algebra-the-borel-algebra-of-a-topology)?

   Zoran #1

   the sigma algebra does not need to be the sigma algebra of Borel subsets on a topological space!

   Does this mean you can answer this MO question?

7. • CommentRowNumber7.
   • CommentAuthorzskoda
   • CommentTimeFeb 8th 2012
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   Author: zskoda
   Format: MarkdownItexLet me come back to that in a couple of days, I do a lecture today and another deadline tomorrow.

   Let me come back to that in a couple of days, I do a lecture today and another deadline tomorrow.