- #1

kolua

- 69

- 3

## Homework Statement

Suppose that the sample space is the set of all real numbers and that every interval of the form (-infinity, b] for any real number b is an event. Show that for any real number b (-infinity, b) must also be an event.

## The Attempt at a Solution

use the 3 conditions required for sigma-algebra.

1. S is an event.

2. If A is an event then A

^{c}is also an event

3. if A

_{a}, A

_{2}... is a countable collection of events, the union of such events is an event.

for the first condition, s is the subset of itself, so it's an event

for the second condition, I am not sure how to prove that [b, infinity) is also an event