Is Limsup of Upper Semicontinuous Function True? Help Needed

MHB
Thread starter ozkan12
Start date Jun 17, 2015

In summary, a limsup (limit supremum) of an upper semicontinuous function is the largest possible value that the function can approach as the input variable approaches a given point. It is calculated by taking the limit of the supremum (least upper bound) of the function as the input variable approaches the given point. The limsup is not always true and depends on the properties and behavior of the function at and near the given point. Understanding the limsup is important in mathematical analysis for describing function behavior and proving the existence of mathematical objects. It has real-world applications in fields such as economics, physics, and engineering, such as modeling stock prices and optimizing solutions.

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 $x\to +\infty$

Related to Is Limsup of Upper Semicontinuous Function True? Help Needed

What is a limsup of an upper semicontinuous function?

A limsup (limit supremum) of an upper semicontinuous function is the largest possible value that the function can approach as the input variable approaches a given point. It is a concept used in mathematical analysis to describe the behavior of a function near a specific point.

How is a limsup calculated?

A limsup of an upper semicontinuous function is calculated by taking the limit of the supremum (least upper bound) of the function as the input variable approaches the given point. This can also be thought of as the highest possible value that the function can reach at or near the given point.

Is the limsup of an upper semicontinuous function always true?

The limsup of an upper semicontinuous function is not always true. It depends on the properties and behavior of the function at and near the given point. In some cases, the limsup may not exist or may be equal to infinity.

Why is it important to understand the limsup of an upper semicontinuous function?

The limsup of an upper semicontinuous function is an important concept in mathematical analysis because it helps to describe the behavior of a function at and near a specific point. It can also be used to prove the existence of certain mathematical objects and to study the properties of different types of functions.

Are there any real-world applications of the limsup of an upper semicontinuous function?

Yes, the limsup of an upper semicontinuous function has various real-world applications in fields such as economics, physics, and engineering. For example, it can be used to model and analyze the behavior of stock prices, temperature fluctuations, and electronic circuits. It is also used in optimization problems to find the best possible solution.