Timeline for $f_\epsilon=\inf\{f(y):|y-x|<\epsilon\}$ is measurable Borel [closed]

10 events

when toggle format	what		by	license	comment
May 18, 2021 at 21:15	history	closed	Gro-Tsen abx Christian Remling Andreas Blass leo monsaingeon		Not suitable for this site
May 15, 2021 at 19:13	vote	accept	Zaragosa
May 15, 2021 at 14:12	answer	added	Gerald Edgar		timeline score: 1
May 15, 2021 at 7:12	history	edited	Zaragosa		edited tags
May 15, 2021 at 7:02	comment	added	Zaragosa		@NateEldredge for the number 2. In the number 1 I found an error, actually I need to prove only this $f_\epsilon(z)\neq a$.
May 15, 2021 at 6:59	history	edited	Zaragosa	CC BY-SA 4.0	added 16 characters in body
May 15, 2021 at 0:45	comment	added	Nate Eldredge		#1 looks fine to me. The boundedness is only needed if you want $f_\epsilon$ to end up being real-valued, and even then you would only need $f$ bounded below. If you allow $f_\epsilon$ to take the value $-\infty$ then it works for unbounded functions too.
May 15, 2021 at 0:15	review	Close votes
May 18, 2021 at 21:15
May 15, 2021 at 0:13	comment	added	Nate Eldredge		For 2, note that for each $x$, $f_\epsilon(x)$ increases as $\epsilon \downarrow 0$, so you can just take the sup over $f_{1/n}(x)$, $n=1,2,3,\dots$. Then it's a sup of a countable set of functions and you are in business.
May 14, 2021 at 23:42	history	asked	Zaragosa	CC BY-SA 4.0