Does the space satisfying following properties exist:

$\{\{B^u_t\}_{0\le t<\infty}:u \in [0,1]\}$,where $\{B^u_t\}_{0\le t<\infty}$ is a standard Brownian motion started from $u$, and they are mutually independent for $u$.

I read Ash,Doléans's book about measure theory in 1999, which says that if I want to construct a product space of uncountable dimension, the "factor" space must have some topological properties. However, I didn't find the results by google.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.