User contributions for Addem
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16 January 2022
- 17:5717:57, 16 January 2022 diff hist 0 m Riesz-Fischer Theorem No edit summary
- 17:3617:36, 16 January 2022 diff hist −2 m Riesz-Fischer Theorem No edit summary
- 17:3317:33, 16 January 2022 diff hist +231 m Riesz-Fischer Theorem house style
- 17:2617:26, 16 January 2022 diff hist +14 m Riesz-Fischer Theorem house style
- 17:1917:19, 16 January 2022 diff hist +62 m Riesz-Fischer Theorem No edit summary
- 17:1717:17, 16 January 2022 diff hist +135 m Riesz-Fischer Theorem house style, adding links
- 17:0417:04, 16 January 2022 diff hist +13 m Riesz-Fischer Theorem Edit for house style
- 16:5716:57, 16 January 2022 diff hist +345 Weierstrass Extreme Value Theorem clarifying f(d)=/=infinity and f(d)=infinity
- 16:4716:47, 16 January 2022 diff hist 0 m Weierstrass Extreme Value Theorem No edit summary
- 16:4216:42, 16 January 2022 diff hist +22 Weierstrass Extreme Value Theorem No edit summary
- 16:4116:41, 16 January 2022 diff hist +10 m Weierstrass Extreme Value Theorem No edit summary
- 16:4016:40, 16 January 2022 diff hist −45 Weierstrass Extreme Value Theorem Using "then" before the statement that f is continuous makes it look like a result, rather than a reiteration of an assumption.
- 16:3816:38, 16 January 2022 diff hist −273 Weierstrass Extreme Value Theorem This is just the definition of the limit being infinity.
- 16:3516:35, 16 January 2022 diff hist +1 m Weierstrass Extreme Value Theorem No edit summary
- 16:2716:27, 16 January 2022 diff hist +4 Weierstrass Extreme Value Theorem Bolzano-Weierstrass should specify that the sequence converges in the universe. I see that on the ProofWiki page for it, the theorem is not stated that way--but that statement is wrong if the sequence is {1/n} taken in (0,1), so the Bolzano-Weierstrass page should be edited.
- 15:5215:52, 16 January 2022 diff hist −52 m Weierstrass Extreme Value Theorem removing sequence brackets
- 15:5015:50, 16 January 2022 diff hist −13 m Weierstrass Extreme Value Theorem Removed sequence brackets, seems to me we're talking about a single point here.
- 15:4115:41, 16 January 2022 diff hist +1,704 Riesz-Fischer Theorem Proof from Folland -- I believe this is the "standard" proof of this theorem
- 15:3515:35, 16 January 2022 diff hist +464 User:Addem/riesz fischer No edit summary current
- 15:2315:23, 16 January 2022 diff hist +522 User:Addem/riesz fischer most of the proof
- 05:5805:58, 16 January 2022 diff hist +1,383 N User:Addem/riesz fischer Created page with "== Theorem == Let $\struct {X, \Sigma, \mu}$ be a measure space. Let $p \in \R$, $p \ge 1$. The Lebesgue $p$-space $\map {\LL^p} \mu$, endowed with the $p$-norm, is a complete metric space. == Proof == To show that $\map {\LL^p} \mu$ is complete we consider an arbitrary norm Cauchy sequence $\{f_n\}$ taken from $\map {\LL^p} \mu$, and demonstrate th..."
14 January 2022
- 19:3919:39, 14 January 2022 diff hist +194 User talk:Addem No edit summary
- 19:3719:37, 14 January 2022 diff hist +8 User:Addem/Holder No edit summary
- 19:3319:33, 14 January 2022 diff hist +89 User:Addem/Holder No edit summary
- 19:2119:21, 14 January 2022 diff hist +3 User:Addem/Holder/Integral No edit summary
- 18:3318:33, 14 January 2022 diff hist 0 User:Addem/Holder/Integral No edit summary
- 18:3218:32, 14 January 2022 diff hist +27 User:Addem/Holder/Integral No edit summary
- 18:3118:31, 14 January 2022 diff hist −3 User:Addem/Holder No edit summary
- 18:3018:30, 14 January 2022 diff hist 0 User:Addem/Holder No edit summary
- 18:2918:29, 14 January 2022 diff hist +29 User:Addem/Holder No edit summary
- 18:2818:28, 14 January 2022 diff hist +11 User:Addem/Holder No edit summary
- 18:2618:26, 14 January 2022 diff hist +2 User:Addem/Holder No edit summary
- 18:2518:25, 14 January 2022 diff hist +298 User:Addem/Holder/Integral No edit summary
- 18:2218:22, 14 January 2022 diff hist +15 User:Addem/Holder/Integral No edit summary
- 18:1918:19, 14 January 2022 diff hist −3 User:Addem/Holder/Integral No edit summary
- 18:1818:18, 14 January 2022 diff hist +188 User:Addem/Holder/Integral No edit summary
- 18:1318:13, 14 January 2022 diff hist +73 User:Addem/Holder/Integral No edit summary
- 18:0818:08, 14 January 2022 diff hist 0 User:Addem/Holder/Integral No edit summary
- 18:0718:07, 14 January 2022 diff hist +107 User:Addem/Holder/Integral No edit summary Tag: Visual edit: Switched
- 18:0018:00, 14 January 2022 diff hist +2,673 N User:Addem/Holder/Integral Created page with "== Theorem == Let $\struct {X, \Sigma, \mu}$ be a measure space. Let $p, q \in \R$ such that $\dfrac 1 p + \dfrac 1 q = 1$. Let $f \in \map {\LL^p} \mu, f: X \to \R$, and $g \in \map {\LL^q} \mu, g: X \to \R$, where $\LL$ denotes Lebesgue space. Then their pointwise product $f g$ is $\mu$-integrable, that is: :$f g \in \map..."
- 17:5817:58, 14 January 2022 diff hist +32 User:Addem/Holder No edit summary
- 17:5517:55, 14 January 2022 diff hist −39 User:Addem/Holder/Summation No edit summary current Tag: Manual revert
- 17:5317:53, 14 January 2022 diff hist +39 User:Addem/Holder/Summation No edit summary
- 17:5317:53, 14 January 2022 diff hist +32 User:Addem/Holder No edit summary
- 17:5117:51, 14 January 2022 diff hist +6 User:Addem/Holder No edit summary
- 17:5117:51, 14 January 2022 diff hist −26 User:Addem/Holder No edit summary
- 17:4917:49, 14 January 2022 diff hist +17 User:Addem/Holder No edit summary Tag: Visual edit: Switched
- 17:4817:48, 14 January 2022 diff hist +2,379 N User:Addem/Holder/Summation Created page with "== Theorem == <onlyinclude> Let $p, q \in \R_{>0}$ be strictly positive real numbers such that: :$\dfrac 1 p + \dfrac 1 q = 1$ Let: :$\mathbf x = \sequence {x_n} \in \ell^p$ :$\mathbf y = \sequence {y_n} \in \ell^q$ where $\ell^p$ denotes the $p$-sequence space. Let $\norm {\mathbf x}_p$ denote the $p$-norm of $\mathbf x$. Then $\mathbf x \mathbf y = \sequence {x_n y_n}..."
- 17:4517:45, 14 January 2022 diff hist −2,832 User:Addem/Holder No edit summary
- 17:3817:38, 14 January 2022 diff hist +3,653 N User:Addem/Holder Created page with "== Hölder's Inequality == There are two theorems which go by the title of Hölder's Inequality, one dealing with summation and the other with integration with respect to a measure. In both cases it is asserted that, when $1\le p\le \infty$ and $q$ is the exponential conjugate of $p$, then $ \|ab\|_1 \le \|a\|_p\|b\|_q $ In the summation case we interpret $\|\cdot \|_p$ as the P-norm and in the integral case we interpret it as The result for summation can be d..."