Question

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

score 118 · Answer 1 · 2026-02-25 23:13:00

118

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

Published on 25 Feb 2026 - 23:13

score 73 · Answer 2 · 2026-04-13 07:24:29

73

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 13 Apr 2026 - 7:24

score 106 · Answer 3 · 2026-02-25 23:09:48

106

Views

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

Published on 25 Feb 2026 - 23:09

score 449 · Answer 4 · 2026-02-25 23:16:42

449

Views

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

Published on 25 Feb 2026 - 23:16

score 67 · Answer 5 · 2026-04-12 22:53:56

67

Views

Show convergence of this infinite product

Published on 12 Apr 2026 - 22:53

score 175 · Answer 6 · 2026-02-25 23:11:45

175

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 25 Feb 2026 - 23:11

score 39 · Answer 7 · 2026-02-25 23:18:05

39

Views

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

Published on 25 Feb 2026 - 23:18

score 94 · Answer 8 · 2026-04-12 17:01:43

94

Views

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

Published on 12 Apr 2026 - 17:01

score 412 · Answer 9 · 2026-04-12 12:25:39

412

Views

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

Published on 12 Apr 2026 - 12:25

score 71 · Answer 10 · 2026-04-12 16:15:16

71

Views

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

Published on 12 Apr 2026 - 16:15

score 99 · Answer 11 · 2026-02-25 23:10:18

99

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 25 Feb 2026 - 23:10

score 231 · Answer 12 · 2026-04-13 04:17:10

231

Views

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

Published on 13 Apr 2026 - 4:17

score 82 · Answer 13 · 2026-04-11 03:11:55

82

Views

Baire functions question

Published on 11 Apr 2026 - 3:11

score 91 · Answer 14 · 2026-04-13 19:05:52

91

Views

The relation between this series and infinitely integral.

Published on 13 Apr 2026 - 19:05

score 116 · Answer 15 · 2026-04-11 03:26:38

116

Views

Combinatorial Families

Published on 11 Apr 2026 - 3:26

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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