Assignment:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.