MHB Is the Pre-Image of a Measurable Function on a Measure Space also Measurable?

[Chris L T521]

Here's this week's problem!

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Problem: Let $f$ be a measurable function on a measure space $(X,\Lambda,\mu)$. Show that the pre-image of any Borel set of $\mathbb{R}$ is also in $\Lambda$.

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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!

 

[Chris L T521]

I will edit this post soon (by this afternoon PST) and update it with the solution then (since it's still being decided upon due to different interpretations).