MHB Limit of upper semicontinuous function

[ozkan12]

for any upper semi continuous how we can take limit ? limit or limsup ? which one is true ?

 

[Ackbach]

for any upper semi continuous how we can take limit ? limit or limsup ? which one is true ?

Well, you're definitely not guaranteed to be able to take the limit. The lim sup is guaranteed to exist, but it's not necessarily equal to the function value at which the function is upper semi-continuous. The wiki is fairly helpful, I think.