Comment. Measurable subsets of R quiz Comment. This quiz is designed to test your knowledge of the sigma-algebra of Lebesgue measurable sets of R and related concepts. Comment. All sets are subsets of the real line R unless otherwise indicated. Shuffle Questions. Shuffle Answers. Question. If E is the union of a Borel set and a null set, the best one can say about E is that it is Answer. A Borel set. Answer. A null set. Correct Answer. A Lebesgue measurable set. Answer. A G_delta set. Answer. A F_sigma set. Answer. An arbitrary set. Answer. A dense set. Question. Let E be a Lebesgue measurable set. Of the true statements listed below, which one is the strongest? Correct Answer. E is equal to a G_delta set with a null set removed. Answer. E is equal to a G_delta set with a null set added. Answer. E is contained in a G_delta set. Answer. E is equal to a G_delta set minus a set of arbitrarily small measure. Answer. E is equal to a G_delta set with a set of arbitrarily small measure added. Answer. E contains a G_delta set. Answer. E is equal to a G_delta set with a null set added and a null set removed. Question. Let E be a Lebesgue measurable set. Of the true statements listed below, which one is the strongest? Correct Answer. E is equal to a F_sigma set with a null set added. Answer. E is equal to a F_sigma set with a null set removed. Answer. E is contained in a F_sigma set. Answer. E is equal to a F_sigma set minus a set of arbitrarily small measure. Answer. E is equal to a F_sigma set with a set of arbitrarily small measure added. Answer. E contains a F_sigma set. Answer. E is equal to a F_sigma set with a null set added and a null set removed. Question. Let E be a Lebesgue measurable set. Of the true statements listed below, which one is the strongest? Answer. E is equal to an open set with a null set added. Answer. E is equal to an open set with a null set removed. Answer. E is contained in an open set. Correct Answer. E is equal to an open set minus a set of arbitrarily small measure. Answer. E is equal to an open set with a set of arbitrarily small measure added. Answer. E is equal to a open set with sets of arbitrarily small measure added and removed. Answer. E is equal to a open set with a null set added and a null set removed. Question. Let E be a Lebesgue measurable set. Of the true statements listed below, which one is the strongest? Answer. E is equal to a closed set with a null set added. Answer. E is equal to a closed set with a null set removed. Answer. E is equal to a closed set with sets of arbitrarily small measure added and removed. Answer. E is equal to a closed set minus a set of arbitrarily small measure. Correct Answer. E is equal to a closed set with a set of arbitrarily small measure added. Answer. E contains a closed set. Answer. E is equal to a closed set with a null set added and a null set removed. Question. Let E be a Lebesgue measurable set of finite measure. Of the true statements listed below, which one is the strongest? Answer. E is equal to a finite union of intervals with a null set added. Answer. E is equal to a finite union of intervals with a null set removed. Correct Answer. E is equal to a finite union of intervals with sets of arbitrarily small measure added and removed. Answer. E is equal to a finite union of intervals minus a set of arbitrarily small measure. Correct Answer. E is equal to a finite union of intervals with a set of arbitrarily small measure added. Answer. E is contained in a finite union of intervals. Answer. E is equal to a finite union of intervals with a null set added and a null set removed. Question. Which of the following classes of sets is NOT closed under countable unions? Answer. The class of null sets. Answer. The class of open sets. Answer. The class of Borel sets. Answer. The class of Lebesgue measurable sets. Correct Answer. The class of G_delta sets. Answer. The class of F_sigma sets. Answer. The class of countable sets.