I was reading the Wikipedia page on Abstract Wiener spaces to get some intuition on the Cameron-Martin spaces. I am really confused with their definition of the "measure" defined on cylindrical sets on a Hilbert space $H$.
- Why is this well defined?
- The article claims that if the Hibert space $H$ is densely embedded into a sufficiently larger separable Banach Space $B$, the same construction can be extended to a (countably-additive) measure on the cylindrical sets of $B$. However, it also claims that $H$ has measure 0, even though the measure is defined by taking the intersection of cylindrical sets in $B$ with $H$.
Any clarification is much appreciated (as well as references).
Thank you!
