 Solution

ID: past-exam-of-the-martingales-and-financial-mathematics-course-of-the-university-of-oxford/2008/a/2/a/i/solution

A real random variable is a measurable map from

(Ω, F)

R

with its Borel sigma-algebra. Equivalently,

{X \leq x} \in F

for every real

x

F (x) = P (X \leq x) .

It is nondecreasing, right-continuous, and tends to zero and one at the two infinities.

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