Letf,g:[a,b]-R, fn:[a,b] → R. and M be the O-algebra of all Lebesgue measurable subsets of [a,b]. Mark all statements th

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Letf G A B R Fn A B R And M Be The O Algebra Of All Lebesgue Measurable Subsets Of A B Mark All Statements Th 1 (25.25 KiB) Viewed 22 times

Letf,g:[a,b]-R, fn:[a,b] → R. and M be the O-algebra of all Lebesgue measurable subsets of [a,b]. Mark all statements that are true. Let f». neN be measurable and E= {xe[a,b] : 1imf(x)exists). Then E is lebesgue measurable. n' n O 0:[0, 1]-R, 4(x) = x.sin(x) is measurable. The function fg: [a,b]-R, (g)(x) =f(x) g(x) is measurable. liff and are measurable then for all a,BER, af +Bg is Lebesgue measurable. + The function 0 : [a,b] → R.Q(x)=sup{f(x): neN},xe[a,b]is measurable. 1 -