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Comment : Countably additive measures
Comment : This quiz is designed to test your knowledge of countably additive measures on a sigma-algebra and related concepts.
Comment : Unless otherwise indicated, (X, A, mu) is a measure space.

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Question 1: If E_n is a sequence of measurable sets in X such that mu(E_n) goes to zero, and f: X -> R is a measurable function, what are the most general conditions under which one can assume the integral of f on E_n also goes to zero?

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	One needs f to be bounded.
	One needs f to be non-negative.
	One needs f to be absolutely integrable.
	One needs the E_n to be nested and decreasing.
	One needs f to be a simple function.
	One needs f to be continuous.
	One needs f to be locally integrable.