Let mu^ be an outer measure on H(R). Then Ein H(R) is mu^-measurable if: where H(R) is a hereditary sigma-ring.

(A) for each Ain H(R), mu^(A)=mu^(Acap E)+mu^(Acap E^C)

Q72Section II (Mathematics)72 of 145

Carath'eodory's criterion: $E$ must split every test set additively

Let $\mu^*$ be an outer measure on $H(\mathbb{R})$ . Then $E\in H(\mathbb{R})$ is $\mu^*$ -measurable if:

where $H(\mathbb{R})$ is a hereditary $\sigma$ -ring.

Pick an option to check your answer.

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