Show that ii implies iii. Theorem 9. The following statements regarding the set E are equivalent:(i) E is measurable.(ii) For all ɛ> 0,30- an open set, OE such that m* (0 – E) ≤ ɛ .ni=1(iii) 3G, a Gs-set, G₂E such that m* (G – E) = 0, (A set G is said to be Gs if G = N G₁,each G is an open set.)(iv) For all ɛ > 0,3 F – a closed set, FCE, such that m* (E – F) ≤ ɛ.8i=1(v) ¨ ³ F, a F-set, F≤E such that m* (E – F) = 0. (A set F is said to be F if F = U F₁,each F is a closed set.)

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Answered: Theorem 9. The following statements…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 1TFE: Label each of the following statements as either true or false. The Well-Ordering Theorem implies...

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Theorem 9. The following statements regarding the set E are equivalent: (i) E is measurable. (ii) For all &> 0,30- an open set, OE such that m* (OE) ≤ε. 00 (iii) 3G, a Gs-set, G2E such that m* (GE) = 0, (A set G is said to be Gs if G = G₁, i=1 each G is an open set.)