 Solution

ID: past-exam-of-the-martingales-and-financial-mathematics-course-of-the-university-of-oxford/2011/a/1/b/i/solution

The intersection of two nonempty members is

(- \infty, x] \cap (- \infty, y] = (- \infty, min (x, y)],

which belongs to the collection. Any intersection involving the empty set is empty and is included too. Hence $π (R)$ is a pi-system.

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