Question

Show that $L^p + L^r$ with the norm $||f|| = \inf \{||g||_p + ||h||_r \ : \ f = g + h\}$ is a Banach space

score 451 · Answer 1 · 2026-04-15 21:38:44

451

Views

Show that $L^p + L^r$ with the norm $||f|| = \inf \{||g||_p + ||h||_r \ : \ f = g + h\}$ is a Banach space

Published on 15 Apr 2026 - 21:38

score 106 · Answer 2 · 2026-04-14 08:06:48

106

Views

Verify the statements for Riemann-integrable function $f_n(x)$.

Published on 14 Apr 2026 - 8:06

score 151 · Answer 3 · 2026-04-15 20:12:48

151

Views

Suppose $[a], [b] \in \mathbb{Z}_n$ and $[a]\cdot[b] = [0]$. Is it necessarily true that either $[a] = [0]$ or $[b] = [0]$?

Published on 15 Apr 2026 - 20:12

score 113 · Answer 4 · 2026-03-25 10:57:26

113

Views

Proving that for $x \ge 17$, $\prod\limits_{p < x\text{, prime, & }p \nmid (x^2+x)}p > x^2 + x$

Published on 25 Mar 2026 - 10:57

score 56 · Answer 5 · 2026-03-26 01:29:15

56

Views

Is my interpretation of this proof of a maximum principle for the discrete heat equation correct?

Published on 26 Mar 2026 - 1:29

score 518 · Answer 6 · 2026-04-15 02:45:13

518

Views

Is this proof that relative entropy is never negative correct?

Published on 15 Apr 2026 - 2:45

score 32 · Answer 7 · 2026-03-25 20:36:40

32

Views

Find a ring homomorphism $\theta$ s.t. Ker $\theta = \mathbb{Z}_6 \times \{[0]\}$.

Published on 25 Mar 2026 - 20:36

score 69 · Answer 8 · 2026-03-28 21:50:39

69

Views

Decomposition group does not depend on the prime

Published on 28 Mar 2026 - 21:50

score 62 · Answer 9 · 2026-04-15 22:53:02

62

Views

Let $f:\Omega\to\textbf{R}^{m}$ be a function. Then $f$ is measurable if and only if $f^{-1}(B)$ is measurable for every open box $B$.

Published on 15 Apr 2026 - 22:53

score 37 · Answer 10 · 2026-03-29 02:45:38

37

Views

Prime inert in each subfields never occurs

Published on 29 Mar 2026 - 2:45

score 80 · Answer 11 · 2026-04-16 01:41:40

80

Views

Let $X$ be a topological space such that $A \subset X$ satisfies

Published on 16 Apr 2026 - 1:41

score 28 · Answer 12 · 2026-04-14 16:59:14

28

Views

Find a solution to the congruences $y \equiv m_1x + b_1 \pmod p$ and $y \equiv m_2x + b_2 \pmod p$

Published on 14 Apr 2026 - 16:59

score 565 · Answer 13 · 2026-04-16 10:44:00

565

Views

Any set $E$ of outer measure zero ($m^{*}(E) = 0$) is measurable.

Published on 16 Apr 2026 - 10:44

score 109 · Answer 14 · 2026-04-13 17:16:38

109

Views

Proof verification: Linear combinations of subsets of the natural numbers generating all multiples of their gcd after a given point

Published on 13 Apr 2026 - 17:16

score 40 · Answer 15 · 2026-04-08 23:53:20

40

Views

Proving limits in terms of epsilon delta questions

Published on 08 Apr 2026 - 23:53

List Question

Show that $L^p + L^r$ with the norm $||f|| = \inf \{||g||_p + ||h||_r \ : \ f = g + h\}$ is a Banach space

Verify the statements for Riemann-integrable function $f_n(x)$.

Suppose $[a], [b] \in \mathbb{Z}_n$ and $[a]\cdot[b] = [0]$. Is it necessarily true that either $[a] = [0]$ or $[b] = [0]$?

Proving that for $x \ge 17$, $\prod\limits_{p < x\text{, prime, & }p \nmid (x^2+x)}p > x^2 + x$

Is my interpretation of this proof of a maximum principle for the discrete heat equation correct?

Is this proof that relative entropy is never negative correct?

Find a ring homomorphism $\theta$ s.t. Ker $\theta = \mathbb{Z}_6 \times \{[0]\}$.

Decomposition group does not depend on the prime

Let $f:\Omega\to\textbf{R}^{m}$ be a function. Then $f$ is measurable if and only if $f^{-1}(B)$ is measurable for every open box $B$.

Prime inert in each subfields never occurs

Let $X$ be a topological space such that $A \subset X$ satisfies

Find a solution to the congruences $y \equiv m_1x + b_1 \pmod p$ and $y \equiv m_2x + b_2 \pmod p$

Any set $E$ of outer measure zero ($m^{*}(E) = 0$) is measurable.

Proof verification: Linear combinations of subsets of the natural numbers generating all multiples of their gcd after a given point

Proving limits in terms of epsilon delta questions

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