I am reading probability theory and I have a question. The Bochner-Minlos theorem roughly says that if we have $E \subset H \subset E^*$ where $H$ is a Hilbert space, then there is a unique measure on $E^*$ satisfying some nice properties.

On the other hand, the Wiener measure is supported on the space of continuous functions. Does that mean Wiener measure is not Bochner-Minlos type of measure? In other words, is the Wiener measure the result of the Bochner-Minlos construction?

I apologize if this question is too simple or doesn't even make sense. I am a beginner in this.

Generalized functions. This volume is written with Vilenkin. In Chapter 3 has a very nice discussion of these issues. $\endgroup$