Let f(x) be a real-valued Lebesgue integrable function on [0, 1]. (a) Prove that if f>...

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Let f(x) be a real-valued Lebesgue integrable function on [0, 1]. (a) Prove that if f> 0 on a set F C [0, 1] of positive measure, then (b) Prove that if [ f(x) dx > 0. F [ f(x) dx = 0, then f(x) = 0 for almost all z = [0, 1]. for each x = [0, 1], Let f(x) be a real-valued Lebesgue integrable function on [0, 1]. (a) Prove that if f> 0 on a set F C [0, 1] of positive measure, then (b) Prove that if [ f(x) dx > 0. F [ f(x) dx = 0, then f(x) = 0 for almost all z = [0, 1]. for each x = [0, 1],

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