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Andrey Rekalo
Andrey Rekalo
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We call u*$u^{*}$ is the upper semicontinuous envelope of u$u$ if it is the smallest upper semicontinuous function satisfying u<=u*$u\le u^*$.

My question is that is there any good properties of the upper semicontinuous envelope of a lower semicontinuous function.

Thank you very much!

We call u* is the upper semicontinuous envelope of u if it is the smallest upper semicontinuous function satisfying u<=u*.

My question is that is there any good properties of the upper semicontinuous envelope of a lower semicontinuous function.

Thank you very much!

We call $u^{*}$ is the upper semicontinuous envelope of $u$ if it is the smallest upper semicontinuous function satisfying $u\le u^*$.

My question is that is there any good properties of the upper semicontinuous envelope of a lower semicontinuous function.

Thank you very much!

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Jiao
Jiao
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The upper semicontinuous envelope of a lower semicontinuous function

We call u* is the upper semicontinuous envelope of u if it is the smallest upper semicontinuous function satisfying u<=u*.

My question is that is there any good properties of the upper semicontinuous envelope of a lower semicontinuous function.

Thank you very much!