Let amp; be an atomic o- algebra generated by a partition ( An )~` ; of a set * ( see Problem 1 ) . 2 ) Fix n gt; 1 . Prove that the function On :...

Please help me prove the following is a measure, where an atomic sigma algebra is the set of all finite or countable unions of members of A (together with ∅)

Let & be an atomic o- algebra generated by a partition ( An )~` ; of a set * ( see Problem1 ) .2 ) Fix n > 1 . Prove that the function On : ~ ~ [0 , 1] defined byOn ( A ) = ]JI if An CATo if An & A( 1 )is a measure on Q .