Simple measure theory questions (inverse image)

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If f-1(E) is measurable, then its complement f-1(E)c is also measurable. This follows from the property that if a set A is measurable, its complement is also measurable. The reasoning is based on the definition of measurable sets in measure theory. The initial statement is confirmed as true by participants in the discussion. The conclusion reinforces the understanding of measurable sets and their complements.
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Homework Statement


I was wondering if we Let E be some set such that f-1(E) is measurable then so is f-1(E)c.

Homework Equations



If the set A is measurable then so is its compliment.

The Attempt at a Solution



I think the statement is true because f-1(E) is just a set and thus its compliment should also be measurable.Thank you for your time.
 
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Yeah that is correct.
 

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