MHB Is Limsup of Upper Semicontinuous Function True? Help Needed

Thread starter ozkan12
Start date Jun 17, 2015

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The discussion centers on whether the limit superior (limsup) of an upper semicontinuous function equals the limit of the function itself. A participant argues that this is not true by providing the example of the continuous function f(x) = sin(x), which has a limsup of 1 as x approaches infinity. The example illustrates that the limsup can differ from the limit of the function. The conversation highlights the need for clarification on the properties of upper semicontinuous functions. Overall, the claim that limsup f(x) equals lim f(x) for upper semicontinuous functions is contested.

Jun 17, 2015

ozkan12

for any upper semicontinuous function limsup f(x)=lim f(x)...Is thıs true ? I don't know, please help me :)

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Jun 17, 2015

Fallen Angel

No,

Just think in $f(x)=sin(x)$, is continuous and its upper limit is 1 when $x\to +\infty$

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