Question

Proof of lower semi-continuity of $x\mapsto \|x\|_{bv}$

score 100 · Answer 1 · 2011-11-24 14:50:14

100

Views

Proof of lower semi-continuity of $x\mapsto \|x\|_{bv}$

Published on 24 Nov 2011 - 14:50

score 6k · Answer 2 · 2012-02-17 21:15:58

6k

Views

Show a function is continuous if and only if it is both upper and lower semi-continuous

Published on 17 Feb 2012 - 21:15

score 1.4k · Answer 3 · 2012-03-22 18:53:25

1.4k

Views

Show that if $f^{-1}((\alpha, \infty))$ is open for any $\alpha \in \mathbb{R}$, then $f$ is lower-semicontinuous.

Published on 22 Mar 2012 - 18:53

score 1.2k · Answer 4 · 2012-03-22 21:39:50

1.2k

Views

The preimage of $(-\infty,a]$ under $f$ is closed for $a \in \mathbb{R}$, then $f$ is semi-continuous.

Published on 22 Mar 2012 - 21:39

score 7.4k · Answer 5 · 2012-03-23 06:24:38

7.4k

Views

Any lower semicontinuous function $f: X \to \mathbb{R}$ on a compact set $K \subseteq X$ attains a min on $K$.

Published on 23 Mar 2012 - 6:24

score 266 · Answer 6 · 2012-05-12 18:06:00

266

Views

Prove that $\{ x: f(x) < a \}$ is an open set. Prove that $\{ x: f(x) = a \}$ is a Borel set.

Published on 12 May 2012 - 18:06

score 6.4k · Answer 7 · 2012-07-02 16:36:34

6.4k

Views

Lower semicontinuous function as the limit of an increasing sequence of continuous functions

Published on 02 Jul 2012 - 16:36

score 984 · Answer 8 · 2012-11-24 13:51:06

984

Views

Pointwise sup of step functions is lower semicontinuous (a.e.)

Published on 24 Nov 2012 - 13:51

score 265 · Answer 9 · 2012-12-11 17:06:21

265

Views

If $\{f_{i}\}_{i\in I}$ are continuous functions $f_{i}:\, X\to\mathbb{R}$ then ${\displaystyle \sup_{i\in I}f_{i}}$ is measurable?

Published on 11 Dec 2012 - 17:06

score 428 · Answer 10 · 2012-12-31 15:09:20

428

Views

lower semicontinuity and closed graph

Published on 31 Dec 2012 - 15:09

score 3.4k · Answer 11 · 2013-01-17 03:35:36

3.4k

Views

Show the iff statement of lower semicontinuous

Published on 17 Jan 2013 - 3:35

score 12.5k · Answer 12 · 2013-01-20 12:46:39

12.5k

Views

Upper semi continuous, lower semi continuous

Published on 20 Jan 2013 - 12:46

score 3.3k · Answer 13 · 2013-02-23 23:39:30

3.3k

Views

Show that the upper semicontinuous has a maximum

Published on 23 Feb 2013 - 23:39

score 101 · Answer 14 · 2013-03-08 18:11:59

101

Views

Lower Semicontinuous functions and Countable Compactness

Published on 08 Mar 2013 - 18:11

score 1.3k · Answer 15 · 2013-03-13 08:55:13

1.3k

Views

Approximation of Semicontinuous Functions

Published on 13 Mar 2013 - 8:55

List Question

Proof of lower semi-continuity of $x\mapsto \|x\|_{bv}$

Show a function is continuous if and only if it is both upper and lower semi-continuous

Show that if $f^{-1}((\alpha, \infty))$ is open for any $\alpha \in \mathbb{R}$, then $f$ is lower-semicontinuous.

The preimage of $(-\infty,a]$ under $f$ is closed for $a \in \mathbb{R}$, then $f$ is semi-continuous.

Any lower semicontinuous function $f: X \to \mathbb{R}$ on a compact set $K \subseteq X$ attains a min on $K$.

Prove that $\{ x: f(x) < a \}$ is an open set. Prove that $\{ x: f(x) = a \}$ is a Borel set.

Lower semicontinuous function as the limit of an increasing sequence of continuous functions

Pointwise sup of step functions is lower semicontinuous (a.e.)

If $\{f_{i}\}_{i\in I}$ are continuous functions $f_{i}:\, X\to\mathbb{R}$ then ${\displaystyle \sup_{i\in I}f_{i}}$ is measurable?

lower semicontinuity and closed graph

Show the iff statement of lower semicontinuous

Upper semi continuous, lower semi continuous

Show that the upper semicontinuous has a maximum

Lower Semicontinuous functions and Countable Compactness

Approximation of Semicontinuous Functions

Trending Questions

Popular # Hahtags

Popular Questions