Let X = R (or any uncountable set). Define µ* : P(X) → R by { if A is countable µ*(A) = 1 if A is uncountable. Then show that µ* is an outer measure but not a measure.
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A: False
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- Consider the function f(x) = ln(x)/x^5. f(x) has a critical number A = __? f"(A) = __? Thus we conclude that f(x) has a local __ at A (type in MAX or MIN).Suppose that w and r are continuous functions on (−∞, ∞), W (x) is an invertible antiderivative of w(x), and R(x) is an antiderivative of r(x). Circle all of the statements that must be true.Consider the uniformly continuous function f(X)=√x on [0,1]. For a given ε>0, what is the largest value of δ>0 in the definition of uniform contiunity? a) ε b) ε2 c) √ε d) ε/2 e) ε-2