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I want to prove the following.

B = {y [tex]\in [/tex] ℝ : μ{f^(-1)(y)} > 0}. I want to prove that B is a countable set.

(to clarify the f^(-1)(y) is the inverse image of y; also μ stands for measure)

Please set me in the right direction. I would greatly appreciate it. Thanks!

**Statement**: Given that f is measurable, letB = {y [tex]\in [/tex] ℝ : μ{f^(-1)(y)} > 0}. I want to prove that B is a countable set.

(to clarify the f^(-1)(y) is the inverse image of y; also μ stands for measure)

Please set me in the right direction. I would greatly appreciate it. Thanks!

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