Stat 6325 Homework 4: Probability Theory, Assignments of Probability and Statistics

Two problems from a university-level statistics course, stat 6325. The first problem asks to show that for any event b in a given probability space and any given ε, there exists an event a in a sub-σ-algebra such that the difference in probabilities between a and b is less than ε. The second problem asks to provide an example of an open cover of the real number interval (0, 1) that does not have a finite subcover.