Consider on (mathbb{R}) the family (Sigma) of all Borel sets which are symmetric w.r.t. the origin. Show

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Consider on \(\mathbb{R}\) the family \(\Sigma\) of all Borel sets which are symmetric w.r.t. the origin. Show that \(\Sigma\) is a \(\sigma\)-algebra. Is it possible to extend a pre-measure \(\mu\) on \(\Sigma\) to a measure on \(\mathscr{B}(\mathbb{R})\) ? If so, is this extension unique? (Problem 9.14 is a continuation of this problem.)

Data from problem 9.14

(Continuation of Problem 6.3) Consider on R the o-algebra  of all Borel sets which are symmetric w.r.t. the

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