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

]]>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?

]]>By the way, under Tannaka duality, it is currently

for A some

algebraicstructure, 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).

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.

]]>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.

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

]]>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.

]]>