Probability/Analysis Question

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

  • Erdos Erdos

    What does \sigma(X) mean here?

  • the σ-algebra generated by X

  • Erdos Erdos

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


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Erdos Erdos
  • Erdos Erdos

    For Doob's Theorem, See page 37 of the following textbook:

  • thanks i'll check it out

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