Measure theory in nuclear spaces Much of the literature on measure theory in linear spaces focuses on the case of normed linear spaces (e.g., the outstanding book by Vakhania, or its sequel). However, nuclear linear spaces "as far from being normed as possible" [nLab], and I haven't been able to find a reference in this setting.
Is there a good reference on measure theory in nuclear spaces?
 A: This subject was studied in some detail in the 70's by the French school, in particular in light of Minlos' theorem and cylindrical measures.  I remember it being a favourite topic in the celebrated "Seminaires".  You can find material in "Radon measures on topological spaces and cylindrical measures" by L. Schwartz, presumably with more detailed references.
A: A good reference, for practical purposes, is Section I.2 of the book "Functional Integration and Quantum Physics" by Barry Simon.

Edit: the above is good for a very light introduction. But in order to go further into probability theory on spaces like $\mathcal{S}, \mathcal{S}',\mathcal{D},\mathcal{D}', \oplus_{\mathbb{N}}\mathbb{R}, \prod_{\mathbb{N}}\mathbb{R}$, etc. I think the best reference is the article "Processus linéaires, processus généralisés" by Fernique. I have also seen references to a book by Dalecky and Fomin, but I don't have access to a copy. 
A: The fourth volume of I. M. Gel'fand's "Generalized Functions", subtitled "Applications of Harmonic Analysis" (written together with N. Ya. Vilenkin and published by Academic Press in 1964, now recently reissued by AMS-Chelsea) discusses this topic abstractly and in depth. It is, in fact, the standard reference for the subject as cited in other books such as J. Glimm's and A. Jaffe's "Quantum Physics - A Functional Integral Approach" (2nd. ed., Springer-Verlag, 1988) and L. Schwartz's book cited in alpha's answer.
It must be said, though, that cylinder set measures as they appear e.g. in the important Bochner-Minlos theorem are actually built over topological duals of nuclear locally convex vector spaces (lcvs).
