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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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