=+The others being obvious, only (iv) needs proof. For a given , choose o-sets B, such that

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=+The others being obvious, only (iv) needs proof. For a given €, choose o-sets B, such that A ,, C UR Bnk and __ P(B ., ) < P*(A,) + €2-", which is possible by the definition (3.1). Now U ,, A ,, C Un .. . Bnk, so that P*(U„ A„) ≤ EnP(B„;)

implies finite subadditivity.

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