Question

A strange process involving a diffeomorphism, a summation and an analytic continuation. Simpler example?

score 117 · Answer 1 · 2020-10-08 13:31:31

117

Views

A strange process involving a diffeomorphism, a summation and an analytic continuation. Simpler example?

Published on 08 Oct 2020 - 13:31

score 71 · Answer 2 · 2020-10-08 16:59:50

71

Views

What's the difference between $\int_{a}^{b} \lim_n f_{n}$ and $\lim_{n \to \infty} \int_{a}^{b} f_{n}$?

Published on 08 Oct 2020 - 16:59

score 105 · Answer 3 · 2020-10-08 22:18:21

105

Views

Check proof that $f_n(x)=x/n$ does not converge uniformly.

Published on 08 Oct 2020 - 22:18

score 448 · Answer 4 · 2020-10-09 18:27:39

448

Views

Show that the sequence of functions is a Cauchy sequence in $L^2[0, 1]$ but not in $C[0,1]$

Published on 09 Oct 2020 - 18:27

score 66 · Answer 5 · 2026-02-25 13:20:30

66

Views

Show convergence of this infinite product

Published on 25 Feb 2026 - 13:20

score 174 · Answer 6 · 2020-10-10 17:00:04

174

Views

Can I say by DCT that $\lim\limits_{n \to \infty} \int_{0}^{1} f_n (x)\ dx = \int_{0}^{1} f(x)\ dx\ $?

Published on 10 Oct 2020 - 17:00

score 38 · Answer 7 · 2020-10-10 17:20:13

38

Views

Prove that $(\mathcal{C}^{(1)}([a,b]),||\cdot||^{(1)})$ is a Banach Space

Published on 10 Oct 2020 - 17:20

score 92 · Answer 8 · 2020-10-10 19:38:26

92

Views

Can we say that $f_n (x) \to f(x),$ as $n \to \infty$ for almost every $x \in [0,1]\ $?

Published on 10 Oct 2020 - 19:38

score 409 · Answer 9 · 2020-10-11 06:20:18

409

Views

A MCQ question about Fourier series appeared in NBHM PhD entrance $2018.$

Published on 11 Oct 2020 - 6:20

score 69 · Answer 10 · 2020-10-11 15:21:32

69

Views

Construct a sequence of choice functions such that their defined well-orders are not isomorphic to each other

Published on 11 Oct 2020 - 15:21

score 98 · Answer 11 · 2020-10-12 10:31:01

98

Views

If a sequence $(u_n)$ in $L^p \cap L^q$ converges to $u$ in $L^p$ and to $v$ in $L^q$, then $u=v$ a.e.

Published on 12 Oct 2020 - 10:31

score 228 · Answer 12 · 2026-02-24 03:28:35

228

Views

Proving $f(x)$ is absolutely continuous on $[a,b].$

Published on 24 Feb 2026 - 3:28

score 79 · Answer 13 · 2020-10-16 02:33:30

79

Views

Baire functions question

Published on 16 Oct 2020 - 2:33

score 88 · Answer 14 · 2020-10-18 05:25:31

88

Views

The relation between this series and infinitely integral.

Published on 18 Oct 2020 - 5:25

score 113 · Answer 15 · 2020-10-18 16:16:17

113

Views

Combinatorial Families

Published on 18 Oct 2020 - 16:16

List Question

A strange process involving a diffeomorphism, a summation and an analytic continuation. Simpler example?

What's the difference between $\int_{a}^{b} \lim_n f_{n}$ and $\lim_{n \to \infty} \int_{a}^{b} f_{n}$?

Check proof that $f_n(x)=x/n$ does not converge uniformly.

Show that the sequence of functions is a Cauchy sequence in $L^2[0, 1]$ but not in $C[0,1]$

Show convergence of this infinite product

Can I say by DCT that $\lim\limits_{n \to \infty} \int_{0}^{1} f_n (x)\ dx = \int_{0}^{1} f(x)\ dx\ $?

Prove that $(\mathcal{C}^{(1)}([a,b]),||\cdot||^{(1)})$ is a Banach Space

Can we say that $f_n (x) \to f(x),$ as $n \to \infty$ for almost every $x \in [0,1]\ $?

A MCQ question about Fourier series appeared in NBHM PhD entrance $2018.$

Construct a sequence of choice functions such that their defined well-orders are not isomorphic to each other

If a sequence $(u_n)$ in $L^p \cap L^q$ converges to $u$ in $L^p$ and to $v$ in $L^q$, then $u=v$ a.e.

Proving $f(x)$ is absolutely continuous on $[a,b].$

Baire functions question

The relation between this series and infinitely integral.

Combinatorial Families

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