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###### Let (R; M /) be the following (familiar) measure space: if E is countable M= {EeR: either E or R E is countable} _ M(E) = otherwise Describe all bounded integrable functions on this measure space and the values of Justify your claims_ Use without proof the description of measurable their integrals functions 0n this kind of space given in the Bonus below. Let (X X 4) be the following measure space: Xis an uncountable set; Bomus. if E is countable I={E â‚¬X: either E or X! E is countable}, M(E) =

Let (R; M /) be the following (familiar) measure space: if E is countable M= {EeR: either E or R E is countable} _ M(E) = otherwise Describe all bounded integrable functions on this measure space and the values of Justify your claims_ Use without proof the description of measurable their integrals functions 0n this kind of space given in the Bonus below. Let (X X 4) be the following measure space: Xis an uncountable set; Bomus. if E is countable I={E â‚¬X: either E or X! E is countable}, M(E) = otherwise R is measurable, then f is 'essentially constant' i.e. there exist If fx+ number for which f = â‚¬. Prove_

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