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 'About the definition of topological manifold using closed sets'

Similar threads

I Apparent counterexample to Cauchy-Goursat theorem (Complex Analysis)

I About the definition of topological manifold using closed sets

I No structure in ##(d,x)## in ##\textbf{Met*}(X)## is admissible

I How are the following three definitions subtly different?

I Convergence not defined by any metric

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Insights What Exactly is Dirac’s Delta Function? - Insight

Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight

Insights Fixing Things Which Can Go Wrong With Complex Numbers