List questions from semicontinuous-functions

Published on 15 Jun 2020 - 12:15

37

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Lower limit and subsequence

Published on 17 Jun 2020 - 8:38

97

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Strong lower semicontinuity theorem

Published on 18 Jun 2020 - 7:50

374

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Prove ceiling function is lower semicontinuous

Published on 13 Sep 2016 - 13:45

2.8k

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Upper semicontinuous function attains its supremum

Published on 11 Oct 2016 - 12:17

590

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Discontinuities of upper semicontinuous function

Published on 17 Oct 2016 - 3:31

212

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For bounded real valued function $f$ show that $\omega_f$ is upper continuous

Published on 20 Nov 2016 - 7:44

1.2k

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Uniform limit of upper semi-continuous functions

Published on 23 Nov 2016 - 19:01

1.4k

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Upper-semicontinuous functions and the condition $\limsup_{x\to p} f(x) \le f(p)$

Published on 26 Dec 2016 - 11:12

268

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Lower-semicontinuous submeasure on $\mathbb N$ vs. function on Cantor space

Published on 29 Dec 2016 - 16:51

108

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Is there a lower semicontinuous function $f:[0,1] \to [0,1] $ such that the set $\{t\in (0,1] : \liminf_{s\nearrow t} f(s) > f(t)\}$ is uncountable?

Published on 08 Feb 2023 - 15:58

45

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Prove that $\operatorname{cl}(\operatorname{epi}(f))\subset\operatorname{epi}(\operatorname{cl}f)$.

Published on 14 Mar 2023 - 7:56

57

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Brezis' Exercise 4.10.1 and 4.10.2

Published on 03 Apr 2023 - 16:35

39

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Semicontinuous Sandwiching of Measurable Functions with Small Integral Difference

Published on 10 Apr 2023 - 7:48

144

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How do I prove these results involving the liminf and the inf ? ( part of a proof on sequential lower semicontinuity of lower semicontinuous envelope)

Published on 03 May 2023 - 20:33

List Question

Regarding ln|f| being upper semicontinuous

Lower limit and subsequence

Strong lower semicontinuity theorem

Prove ceiling function is lower semicontinuous

Upper semicontinuous function attains its supremum

Discontinuities of upper semicontinuous function

For bounded real valued function $f$ show that $\omega_f$ is upper continuous

Uniform limit of upper semi-continuous functions

Upper-semicontinuous functions and the condition $\limsup_{x\to p} f(x) \le f(p)$

Lower-semicontinuous submeasure on $\mathbb N$ vs. function on Cantor space

Is there a lower semicontinuous function $f:[0,1] \to [0,1] $ such that the set $\{t\in (0,1] : \liminf_{s\nearrow t} f(s) > f(t)\}$ is uncountable?

Prove that $\operatorname{cl}(\operatorname{epi}(f))\subset\operatorname{epi}(\operatorname{cl}f)$.

Brezis' Exercise 4.10.1 and 4.10.2

Semicontinuous Sandwiching of Measurable Functions with Small Integral Difference

How do I prove these results involving the liminf and the inf ? ( part of a proof on sequential lower semicontinuity of lower semicontinuous envelope)

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