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    Sigma Algebra and Inverse Imaging

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    Let f : X -> Y be any function. Let sigma (Y ) be a sigma-algebra on Y .

    Show that
    {f −1 (B ) : B E sigma (Y )}
    is a sigma-algebra on X. f −1 (B ) is the inverse image of B , that is
    {x : f (x) E B }.

    Where E represents the 'belongs to' symbol.

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