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Real Analysis : Sigma-algebra

Suppose X is a measurable space, E belongs to the sigma algebra ( I believe to the sigma algebra in X) , let us consider XE = Y. Show that all sets B which can be expressed as AE, where A belongs to the sigma algebra in X, form a sigma-algebra in Y.
Please justify every step and claim you make in the solution.

Solution Summary

A sigma-algebra is investigated. The solution is detailed and well presented.

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