## Question

###### 3.) a) Let D and E be measurable sets and f a function with domain D U E. Show that f is measurable if and only if its restriction to D and E are measurable_b.) Let f be a function with measurable domain D_ Show that f ismeasurable if and only if the function g defined by g(x) = f (x) for x â‚¬ D and g (x) 0 for x â‚¬ D is measurable_

3.) a) Let D and E be measurable sets and f a function with domain D U E. Show that f is measurable if and only if its restriction to D and E are measurable_ b.) Let f be a function with measurable domain D_ Show that f is measurable if and only if the function g defined by g(x) = f (x) for x â‚¬ D and g (x) 0 for x â‚¬ D is measurable_

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