Probability Spaces

An introduction to analysis usually begins with a study of properties of ℝ, the set of real numbers. It will be assumed that you know something about them. More specifically, it is assumed that you realize that (i)they form a field (which means that you can add, multiply, subtract and divide in the usual way),and(ii)they are (totally) ordered (i.e., for any two numbers a, b ∈ ℝ, either a < b, a = b, or a> b) and a ≥ b if and only if a - b ≥ 0. Note that a < b and 0 < c imply ac < bc; a ≤ b imply a + c ≤ b + c for any c ∈ ℝ; 0 < 1 and - 1 < 0.