query: Measure of $\lbrace (x_1,...,x_n) \in \mathbb{R}^n : \sum_{k=1}^{n} x_k \leq 1 \rbrace$
positive_passages.docid: 22573
positive_passages.text: Volume of $T_n=\{x_i\ge0:x_1+\cdots+x_n\le1\}$
negative_passages.docid: 63124
negative_passages.text: Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
negative_passages.docid: 53244
negative_passages.text: Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
negative_passages.docid: 123806
negative_passages.text: How do I show that the integral of $e^{inx}$ over a set of measure $1$ is nonzero for some nonzero $n$?
negative_passages.docid: 77510
negative_passages.text: $\sum_{1}^{n}\left ( a_{i}b_{i} \right )\geq \prod_{1}^{n}\left ( a_{i}^{b_{i}} \right )$
negative_passages.docid: 36485
negative_passages.text: $H_n(X,A) \not \approx \tilde{H}_n(X/A)$
negative_passages.docid: 43188
negative_passages.text: The $n^{th}$ root of the geometric mean of binomial coefficients.
negative_passages.docid: 110222
negative_passages.text: Maximal inequality for a sequence of partial sums of independent random variables
negative_passages.docid: 19804
negative_passages.text: How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
negative_passages.docid: 127047
negative_passages.text: How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
negative_passages.docid: 136737
negative_passages.text: Proof by Induction for inequality, $\sum_{k=1}^nk^{-2}\lt2-(1/n)$
negative_passages.docid: 155974
negative_passages.text: Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
negative_passages.docid: 27901
negative_passages.text: Proving $\sum\limits_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot \|y\|$
negative_passages.docid: 153272
negative_passages.text: Basic question about $\sup_{x\neq 0}{} \frac{\|Ax\|}{\|x\|} = \sup_{\|x\| = 1}{\|Ax\|} $, $x \in\mathbb{R}^n$
negative_passages.docid: 99562
negative_passages.text: "Sum" of positive measure set contains an open interval?
negative_passages.docid: 92175
negative_passages.text: Given $y_n=(1+\frac{1}{n})^{n+1}$ show that $\lbrace y_n \rbrace$ is a decreasing sequence
negative_passages.docid: 63313
negative_passages.text: Uniqueness of Powerseries in an arbitrarily small neighborhood of $0$ in $\mathbb C$