4. Let fig E m" and a ER. Then af, f V 9, f1g, ft, f , and If are all in m". Moreover, if f +9 is defined a.e., then f +

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4 Let Fig E M And A Er Then Af F V 9 F1g Ft F And If Are All In M Moreover If F 9 Is Defined A E Then F 1 (8.56 KiB) Viewed 23 times

4 Let Fig E M And A Er Then Af F V 9 F1g Ft F And If Are All In M Moreover If F 9 Is Defined A E Then F 2 (22.59 KiB) Viewed 23 times

4 Let Fig E M And A Er Then Af F V 9 F1g Ft F And If Are All In M Moreover If F 9 Is Defined A E Then F 3 (22.59 KiB) Viewed 23 times

4. Let fig E m" and a ER. Then af, f V 9, f1g, ft, f , and If are all in m". Moreover, if f +9 is defined a.e., then f + g em".
Tha the. fvg= fugix) = max{ f (xs, glxi? fig = fA gent = min{ foar, goei? = 7 ft - foni- max{f(xi,o} f = f(x) = -minfo , f exi} (Def). An extended real valued function of that is defined are on R is said to be Lebesque measurable, or simply measurable, if there exists a sequence (On100 CM s.t. lim Pu (x1= f(x) are We denote the class of all such ts by mi r m ию r