# Probability/Analysis Question

Suppose X : R ? R is a Borel random variable, and suppose that the image of X is in Q. Show that ?(X) is not the whole Borel ?-algebra.

• What does \sigma(X) mean here?

• the σ-algebra generated by X

• σ(X) is the smallest sigma algebra F such that X is a measurable function? I see.

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