List questions from supremum-and-infimum

Published on 17 Apr 2021 - 12:42

64

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Letting $\varepsilon \to 0$ in proofs

Published on 17 Apr 2021 - 16:39

61

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Is C_b((a,b)) a complete metric space?

Published on 21 Apr 2021 - 17:48

59

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Assistance: "Two functions, prove uniform conv. using sup-norm"

Published on 21 Apr 2021 - 20:46

782

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Let $x_n\leq y_n$ for each $n\in \Bbb N$. Show that $\liminf x_n \leq \liminf y_n$

Published on 22 Apr 2021 - 14:06

116

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Prove that $M_{|f|}-m_{|f|} \le M_f-m_f$

Published on 22 Apr 2021 - 17:03

72

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Exchanging the expectation and supremum

Published on 27 Mar 2026 - 3:58

350

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Prove: If $f$ is integrable, than $|f|$ is integrable

Published on 23 Apr 2021 - 5:14

108

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$\sup\{\frac{1}{f(x)}|x\in[a,b]\} = \frac{1}{\inf\{f(x)|x\in[a,b]\}}$: but is it?

Published on 06 Apr 2026 - 14:42

271

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Prove that $\sup(AB) = \sup(A)\cdot \sup(B)$

Published on 24 Apr 2021 - 8:42

29

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Sum of a normally distributed rv and a Bernouilli distributed rv

Published on 05 Apr 2026 - 20:17

109

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Calculate sup and inf of $A=\{n/(1-n^2)\mid n>1\}.$

Published on 26 Apr 2021 - 20:15

96

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Find infimum and closure of $A$

Published on 26 Apr 2021 - 20:40

91

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Prove the following statements. (a) $\|fg\|_u \le \|f\|_u\|g\|_u$; (b) $\sup_{n\in N} \|f_n\|_u < \infty$

Published on 28 Apr 2021 - 2:44

44

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How to show first property of norm?

Published on 28 Apr 2021 - 22:04

List Question

$\sup(A \cdot B) = \sup A \sup B$

Letting $\varepsilon \to 0$ in proofs

Is C_b((a,b)) a complete metric space?

Assistance: "Two functions, prove uniform conv. using sup-norm"

Let $x_n\leq y_n$ for each $n\in \Bbb N$. Show that $\liminf x_n \leq \liminf y_n$

Prove that $M_{|f|}-m_{|f|} \le M_f-m_f$

Exchanging the expectation and supremum

Prove: If $f$ is integrable, than $|f|$ is integrable

$\sup\{\frac{1}{f(x)}|x\in[a,b]\} = \frac{1}{\inf\{f(x)|x\in[a,b]\}}$: but is it?

Prove that $\sup(AB) = \sup(A)\cdot \sup(B)$

Sum of a normally distributed rv and a Bernouilli distributed rv

Calculate sup and inf of $A=\{n/(1-n^2)\mid n>1\}.$

Find infimum and closure of $A$

Prove the following statements. (a) $\|fg\|_u \le \|f\|_u\|g\|_u$; (b) $\sup_{n\in N} \|f_n\|_u < \infty$

How to show first property of norm?

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