Question

Show $ f_n\xrightarrow{L^1}f\iff f_n\to f \text{ in measure} \iff f_n\to f \text{ almost uniformly} \iff f_n\to f \text{ a.e.}$

score 88 · Answer 1 · 2026-04-15 17:35:56

88

Views

Show $ f_n\xrightarrow{L^1}f\iff f_n\to f \text{ in measure} \iff f_n\to f \text{ almost uniformly} \iff f_n\to f \text{ a.e.}$

Published on 15 Apr 2026 - 17:35

score 75 · Answer 2 · 2026-04-13 19:14:57

Is it always needed to go through bi-conditionals in separated steps when proving equivalence? Proving $A \subseteq B \Leftrightarrow B' \subseteq A'$

score 171 · Answer 3 · 2026-04-14 14:40:44

171

Views

Calculation with Landau symbol (Big $O$)

Published on 14 Apr 2026 - 14:40

score 96 · Answer 4 · 2026-04-14 10:53:09

96

Views

Invertible and compact operators

Published on 14 Apr 2026 - 10:53

score 56 · Answer 5 · 2026-04-17 04:09:21

56

Views

Integrability of $f(x,y)=\frac{(x+y)\log(y/x)}{(xy)^{a}(1+x^2+y^2)}$ on $O=\{(x,y):x>0,y>0\}.$

Published on 17 Apr 2026 - 4:09

score 17 · Answer 6 · 2026-04-16 03:59:00

17

Views

Groups such that the corresponding algebra is central

Published on 16 Apr 2026 - 3:59

score 33 · Answer 7 · 2026-04-17 11:13:42

33

Views

Given connected $(X,O)$ space , $\emptyset \ne A \subseteq X$ and $\partial(A)=\emptyset$: Show, $A = X$

Published on 17 Apr 2026 - 11:13

score 751 · Answer 8 · 2026-04-16 08:36:24

751

Views

Prove that every sequence of real numbers has at least one limit point

Published on 16 Apr 2026 - 8:36

score 156 · Answer 9 · 2026-04-16 02:00:41

156

Views

One nappe of the hyperbola is an embedding. Pollack 1.3.8

Published on 16 Apr 2026 - 2:00

score 123 · Answer 10 · 2026-04-14 02:22:15

123

Views

Proof Verification: Distance Topology on $\mathbb{R}$

Published on 14 Apr 2026 - 2:22

score 418 · Answer 11 · 2026-04-11 14:34:11

418

Views

Independence of two random variables (by checking joint generating function)

Published on 11 Apr 2026 - 14:34

score 519 · Answer 12 · 2026-04-13 19:06:09

519

Views

Proof verification: Prove V is infinite-dimensional iff there exists an infinite sequence

Published on 13 Apr 2026 - 19:06

score 639 · Answer 13 · 2026-04-16 08:37:05

639

Views

Prove that for all sets A and B, A ∩ B = ∅ implies ( A ∪ B ) - B = A

Published on 16 Apr 2026 - 8:37

score 125 · Answer 14 · 2026-04-11 04:27:41

125

Views

Root Field of $x^4 +ax^2 + b$

Published on 11 Apr 2026 - 4:27

score 654 · Answer 15 · 2026-04-16 02:59:10

654

Views

Let $L$ be the line $y = mx$, where $m \neq 0$. Find an expression for $T(x,y)$, where $T$ is the reflection of $\textbf{R}^{2}$ about $L$.

Published on 16 Apr 2026 - 2:59

List Question

Show $ f_n\xrightarrow{L^1}f\iff f_n\to f \text{ in measure} \iff f_n\to f \text{ almost uniformly} \iff f_n\to f \text{ a.e.}$

Is it always needed to go through bi-conditionals in separated steps when proving equivalence? Proving $A \subseteq B \Leftrightarrow B' \subseteq A'$

Calculation with Landau symbol (Big $O$)

Invertible and compact operators

Integrability of $f(x,y)=\frac{(x+y)\log(y/x)}{(xy)^{a}(1+x^2+y^2)}$ on $O=\{(x,y):x>0,y>0\}.$

Groups such that the corresponding algebra is central

Given connected $(X,O)$ space , $\emptyset \ne A \subseteq X$ and $\partial(A)=\emptyset$: Show, $A = X$

Prove that every sequence of real numbers has at least one limit point

One nappe of the hyperbola is an embedding. Pollack 1.3.8

Proof Verification: Distance Topology on $\mathbb{R}$

Independence of two random variables (by checking joint generating function)

Proof verification: Prove V is infinite-dimensional iff there exists an infinite sequence

Prove that for all sets A and B, A ∩ B = ∅ implies ( A ∪ B ) - B = A

Root Field of $x^4 +ax^2 + b$

Let $L$ be the line $y = mx$, where $m \neq 0$. Find an expression for $T(x,y)$, where $T$ is the reflection of $\textbf{R}^{2}$ about $L$.

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