Question: By a direct argument (that is, by using the definition of measurability), show that, if X and y are r.v.s, then so are the mappings

By a direct argument (that is, by using the definition of measurability), show that, if X and y are r.v.s, then so are the mappings X ( Y, XY, and X/Y (Y ( 0 a.s.; i.e., Y ( 0 with probability 1, or Y ( 0 almost surely).

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