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N→∞ g n(x) = F0(x) for almost every x ∈ a,b, by the Lebesgue dominated convergence theorem, we see that for each c ∈ a,b, Z c a F0(x)dx = lim n→∞ Z c a g n(x)dx But F is continuous;Note that (f B g)(x) ≠ (g B f)(x) This means that, unlike multiplication or addition, composition of functions is not a commutative operation The following example will demonstrate how to evaluate a composition for a given value Example 6 Find (f B g)(3) and (g B f)(3) if f ( x ) = x 2 and g ( x ) = 4 – x2 Solution Step 1 Find (f X p { E ŃW F j t @ E y X Ƌ V L 0 N ̎ ܎ V Y 剉 D ܂𑍂Ȃ߂ɂ ŁA S Ă̎ ܎ ɃX ȃV G b g ̃h X œo ꂵ l E E F K ́A ɃX e B Ń_ X 𓾈ӂɂ 邱 ƂŒm 鑶 ݁B 2 l Ƃ L A ł ƃX ȃ{ f B ێ Ă 鑶 ݂ł A l ʐ^ E SAG A h 5 L ̃g t B Ў Ŏ グ Ă l q ʂ A g h E A ̂ ߂ɕs Ȃ̂ E F C g g g j O B

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Chapter 8 Integrable Functions 81 Definition of the Integral If f is a monotonic function from an interval a,b to R≥0, then we have shown that for every sequence {Pn} of partitions on a,b such that {µ(Pn)} → 0, and every sequence {Sn} such that for all n ∈ Z Sn is a sample for Pn, we have {X (f,Pn,Sn)} → Abaf 81 Definition (Integral) Let f be a bounded function from an intervalC higan D e pt o f N a t u r a l R e s o u r c e s 5 0 1 3 M i c h i g a n D e ptofJulie A N a t u r a l R e s o u r c e s 4 9 9 2 Owner?C Ⴂ C Œb ꂽ Y ̃E F b g X c ł ~ t X c A O W W P b g Z b g A b v Ƃ ɐō ݁E I _ ~ B f ނ g p R X g p t H } X E F b g X c ł B

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REAL ANALYSIS I HOMEWORK 3 2 then we have x= X n2N b n3 n X n2N c n 2 3 n X n2N b n3 n 1 2 X n2N c n3 n2C C=2 since (b n) and (c n) are sequences of 0's and 2'sAs xwas arbitrary above, we obtain 0;1 A B Hence m(A B) 1, but nd Bare closed sets of measure zeroAuthor Created Date PMAnswer (1 of 7) I would argue that you are not providing sufficient data for obtaining any one single correct answer You must determine more variables Let me show you Mathematically, you have already defined A as E, which means (obviously) that E is also A Thus, E

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