Question

$\| f \|_{BV} = | f(a) | + V_{a}^{b} f$ defines a norm in the space $BV[a,b]$

score 510 · Answer 1 · 2015-12-15 10:07:58

510

Views

$\| f \|_{BV} = | f(a) | + V_{a}^{b} f$ defines a norm in the space $BV[a,b]$

Published on 15 Dec 2015 - 10:07

score 87 · Answer 2 · 2015-12-15 21:45:51

87

Views

If $\| f_n - f \|_{BV} \rightarrow 0$, then $f_n$ converges uniformly to $f$ on $[a, b]$

Published on 15 Dec 2015 - 21:45

score 408 · Answer 3 · 2016-01-01 09:47:55

408

Views

Relationship between functions of bounded variation and signed measures

Published on 01 Jan 2016 - 9:47

score 894 · Answer 4 · 2016-01-23 23:48:54

894

Views

If $f$ is of bounded variation on $[a+\epsilon, b]$, does it imply $f$ is of bounded variation on $[a,b]$?

Published on 23 Jan 2016 - 23:48

score 37 · Answer 5 · 2016-01-26 00:22:13

37

Views

Show that $V_{a}^{b}(X_\mathbb{Q}) = +\infty$ on any interval [a, b]

Published on 26 Jan 2016 - 0:22

score 89 · Answer 6 · 2016-01-26 15:40:27

89

Views

Given $f(x) = x^{1/3}$, show that $f \in BV[0, 1]$

Published on 26 Jan 2016 - 15:40

score 126 · Answer 7 · 2016-02-02 15:23:45

126

Views

Wrong result: a continuous function has zero $p$-variation, for every $p$. Where's the error?

Published on 02 Feb 2016 - 15:23

score 5.4k · Answer 8 · 2016-02-03 05:45:42

5.4k

Views

Does differentiability imply having bounded variation on some subinterval?

Published on 03 Feb 2016 - 5:45

score 743 · Answer 9 · 2016-02-04 11:25:35

743

Views

Construct a non-monotone continuous function of bounded variation

Published on 04 Feb 2016 - 11:25

score 1.1k · Answer 10 · 2016-02-06 21:29:16

1.1k

Views

Decomposition of function of bounded variation

Published on 06 Feb 2016 - 21:29

score 135 · Answer 11 · 2016-02-07 14:12:49

135

Views

When is the Stieltjes integral of bounded variations?

Published on 07 Feb 2016 - 14:12

score 67 · Answer 12 · 2016-02-16 00:43:23

67

Views

Construct a continuous function $f$ with $0\leq f\leq 1$ such that $\int_a^bf d\alpha\geq\alpha(d)-\alpha(c)-\epsilon$

Published on 16 Feb 2016 - 0:43

score 434 · Answer 13 · 2016-02-22 19:53:23

434

Views

Real Analysis, Folland problem 3.5.27 Functions of Bounded Variation

Published on 22 Feb 2016 - 19:53

score 802 · Answer 14 · 2016-03-02 13:34:42

802

Views

How to show that $BV[0,1]$, the space of all functions on $[0,1]$ of bounded variation, is not complete under the supremum norm?

Published on 02 Mar 2016 - 13:34

score 959 · Answer 15 · 2016-03-04 21:56:29

959

Views

A function with rectifiable graph satisfies Lipschitz condition on a large set

Published on 04 Mar 2016 - 21:56

List Question

$\| f \|_{BV} = | f(a) | + V_{a}^{b} f$ defines a norm in the space $BV[a,b]$

If $\| f_n - f \|_{BV} \rightarrow 0$, then $f_n$ converges uniformly to $f$ on $[a, b]$

Relationship between functions of bounded variation and signed measures

If $f$ is of bounded variation on $[a+\epsilon, b]$, does it imply $f$ is of bounded variation on $[a,b]$?

Show that $V_{a}^{b}(X_\mathbb{Q}) = +\infty$ on any interval [a, b]

Given $f(x) = x^{1/3}$, show that $f \in BV[0, 1]$

Wrong result: a continuous function has zero $p$-variation, for every $p$. Where's the error?

Does differentiability imply having bounded variation on some subinterval?

Construct a non-monotone continuous function of bounded variation

Decomposition of function of bounded variation

When is the Stieltjes integral of bounded variations?

Construct a continuous function $f$ with $0\leq f\leq 1$ such that $\int_a^bf d\alpha\geq\alpha(d)-\alpha(c)-\epsilon$

Real Analysis, Folland problem 3.5.27 Functions of Bounded Variation

How to show that $BV[0,1]$, the space of all functions on $[0,1]$ of bounded variation, is not complete under the supremum norm?

A function with rectifiable graph satisfies Lipschitz condition on a large set

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