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Measure Theory/Probability. Solve the following: 6.1 We say that a subset V C N has Cesaro-density if the next limit lim # ( Vn [0,

Measure Theory/Probability.

Solve the following:

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6.1 We say that a subset V C N has Cesaro-density if the next limit lim # ( Vn [0, n] ) =: p(V) n exists. Let C C 2N (subset of subsets of N) such that p( V ) exists for every V E C. Show that there are sets V1, V2 E C such that Vin V2 & C (C is not a o-algebra)

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