Problem 6 (10pt). Let F ( ti\" be a measurable set and F : E A R5 be a vector valued function defined on E. We write F = (f1,f2, . .. , ff), where f}; : E e R is the i-th component of F. F is said to be measurable if for all open sets U C RE, F'1(U) is measurable. Show that F is measurable if and only if 3'}; is measurable for all 1 g n g E. 1