MHB Limit of upper semicontinuous function

ozkan12 · Jun 20, 2015

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

Ackbach · Jun 26, 2015

ozkan12 said:

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.

MHB Limit of upper semicontinuous function

Thread 'Apparent counter-example to Cauchy-Goursat theorem (Complex Analysis)'

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