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1) Let A CR satisfy m*(A) < ∞o. Prove that there exists a Gs set G where m* (A) = m* (G). Hint: Look at m* (A) + 1/n for every n E N and use the definition of inf and m* to obtain an open set Gn where AC Gn and m* (Gn) < m* (A) + 1/n. The way to define the G should now be pretty obvious (and the fact G is Gs should be immediate).

1) Let A CR satisfy m*(A) < ∞o. Prove that there exists a Gs set G where m* (A) = m* (G). Hint: Look at m* (A) + 1/n for every n E N and use the definition of inf and m* to obtain an open set Gn where AC Gn and m* (Gn) < m* (A) + 1/n. The way to define the G should now be pretty obvious (and the fact G is Gs should be immediate).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 29E
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1) Let A CR satisfy m*(A) < ∞o. Prove that there exists a Gs set G where m* (A) = m* (G). Hint: Look at m* (A) + 1/n for every n E N and use the definition of inf and m* to obtain an open set Gn where AC Gn and m* (Gn) < m* (A) + 1/n. The way to define the G should now be pretty obvious (and the fact G is Gs should be immediate).
Transcribed Image Text:1) Let A CR satisfy m*(A) < ∞o. Prove that there exists a Gs set G where m* (A) = m* (G). Hint: Look at m* (A) + 1/n for every n E N and use the definition of inf and m* to obtain an open set Gn where AC Gn and m* (Gn) < m* (A) + 1/n. The way to define the G should now be pretty obvious (and the fact G is Gs should be immediate).
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