The Wikipedia article on Classical Wiener space states that:

classical Wiener measure γ is the radonification of the canonical Gaussian cylinder set measure on the Cameron-Martin Hilbert space corresponding to $C_0$

Could anyone provide a reference explaining the whole thing?

  • $\begingroup$ Is there any particular reason to not just view it as the law of Brownian motion? $\endgroup$ – Ian Aug 7 '16 at 16:27
  • $\begingroup$ Both, actually. I know some measure theory, but don't really recognise any of the concepts involved: that is, radonification of a measure, Gaussian cylinder set measure or the Cameron-Martin Hilbert space. EDIT: Wrote this in reply to a comment (which apparently is no longer there) asking whether I want to know what a Wiener measure is, or learn how to read this particular definition. $\endgroup$ – rorszaq Aug 7 '16 at 16:30
  • $\begingroup$ I removed that comment because I checked the article and saw that technically the article is about a more general object than just $n$-dimensional Brownian motion. I think the definition in the OP works in this more general setting while the more common definition (define on cylindric sets, extend from there) doesn't. $\endgroup$ – Ian Aug 7 '16 at 17:08
  • $\begingroup$ There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs. $\endgroup$ – Did Aug 10 '16 at 6:33

I don't know if it will be able to explain precisely this statement, but a good reference is chapter 8 of Stroock's Probability Theory: An Analytic View.


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