1. Let ECR. Prove that E is Lebesgue measurable if and only if it satisfies the...

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1. Let ECR. Prove that E is Lebesgue measurable if and only if it satisfies the Caratheodory's condition': For every ACR, it is true that |A| = |ANE|+|AN], where = R \ E. 1. Let ECR. Prove that E is Lebesgue measurable if and only if it satisfies the Caratheodory's condition': For every ACR, it is true that |A| = |ANE|+|AN], where = R \ E.