This is excellent. Amazing (equation + picture)/text ratio. Complaint: you don't define your notion of "space". In chapter 1 it's some informal notion that you

This is excellent. Amazing (equation + picture)/text ratio. Complaint: you don't define your notion of "space". In chapter 1 it's some informal notion that you use to motivate the definition of a set (??), in 1.3 and 1.4 it becomes clear by space you mean "set". Then later you start talking about dimension of spaces, implying not only do they come with a topology now they have a well defined dimension, so a locally Euclidean Hausdorff space or something - but maybe you just mean R^n. Comment for other commentators in this thread: not all expositions is tailored for the masses. A piece of pedagogical literature that does not appeal to your background doesn't mean it's not good. There's a very clear need for exposition on basic structures in probability theory and this fits there.