Which probability measures on $\mathbf{\mathcal{C}[0,1]}$ are known? (Here $\mathcal{C}[0,1]$ is the space of continuous real-valued functions defined on the unit interval.)
I'm pretty sure the Wiener measure (or maybe it's "a" Wiener measure) is one such measure whose random elements are Brownian motion paths (or something like that, please correct me if this, or anything else I've said, is incorrect). Where can I read about the Wiener measure as a measure (instead of just a process with an implicit measure; I want explicit analysis of the measure)? Planet math has a little bit about this, but I'd like more detail.
To answer my "where can I read..." question, feel free to just give an explanation yourself, if you're so inclined.
Edit. At the behest of Nate (see the comments) I'll try to be more explicit. In Cantor space, $\{0,1\}^{\mathbb{N}}$, the uniform (i.e. Lebesgue) measure is the most natural. Is there a most natural measure in $\mathbf{\mathcal{C}[0,1]}$? After that, the Bernoulli measures are most natural measures on Cantor space. So I'd like some examples of "natural" measures on $\mathcal{C}[0,1]$. As Nate said in his comment, the space of measures is the same as the space of continuous processes. Since I'm not so "process-inclined", I'd prefer answers and references to be in the language of measures rather than processes. However, if there's a process that is very natural (or at least important), but who's corresponding measure is harder to work with and therefore unavailable in the literature, a reference to or description of that process will still be appreciated.
Nate's comment also led to this question, an answer to which might render void my request for answers to be in the language of measures:
What exactly is the correspondence between measures and continuous stochastic processes?