on [a b]. a measure set and ut an a measure onN to M А" А*l cЕ. 111- Let & be a continuous function on [a, b]. show that

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on [a b]. a measure set and ut an a measure onN to M А" А*l cЕ. 111- Let & be a continuous function on [a, b]. show that I it is integrable 12- show that unit point mass function at a is a on X: 13- Let & be a outer measure on X. Denot by M, the collection of all ut measurable subsets of Then (is M is a 6-algebra, and ( XM). (ii) the restriction of is 14 show that: interval in R is measurable. (6) Every open set in R is measurable. closed set in IR is measurable. in Every set that is a countable intersection of open in IR is measurable. 15- Let (2 E) be a measurable space and EEE and f: ER. Give three conditions which are equivalent to measurability of f, with proof. 16- bet (x, E, ly be a measure space and of a measut rable function on Z. Define the Lebesgue integral off on x in detail. i) Every (c) Every