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Let M be the family of Lebesgue measurable subsets [a,b] and f:[a,b] → R. Mark all statements that are true. OR?:[a,b] →
Posted: Thu May 12, 2022 8:51 am
by answerhappygod
- Let M Be The Family Of Lebesgue Measurable Subsets A B And F A B R Mark All Statements That Are True Or A B 1 (36.71 KiB) Viewed 51 times
Let M be the family of Lebesgue measurable subsets [a,b] and f:[a,b] → R. Mark all statements that are true. OR?:[a,b] → R given by f2(x)=(f(x))2 is Lebesgue measurable. Olet V[0,1]be the Vitali's set and Xv:[0,1]+R be the characteristic function (1 ifx eV of V, that is, Xv(x) if x €[0,1]\V Then Xy is measurable. Olet Cs[0,1] be the Cantor tertiary set and Xc:[0,1] R be the characteristic function 1 if x EC of C, that is, Xc(X) = O ifx E[0,1]ıc Then X c is measurable. Olet g: [a,b] → R and assume that 1g|:[a,b] R, 1g|(x)=lg(x)] is measurable. Then gis measurable. Of is measurable if and only if f-1(a,)) E M for all a ER.