query: Relation between $X\in L^p$ and $n^{-1/p}\sum X$ for i.i.d. sequence.
positive_passages.docid: 117912
positive_passages.text: How to show that $p$th moment being finite is equivalent to a limit existing
negative_passages.docid: 93806
negative_passages.text: $\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
negative_passages.docid: 114315
negative_passages.text: The sequence 1/(n-1) is apparently unbounded yet convergent. What am I missing here?
negative_passages.docid: 55464
negative_passages.text: Convergence of sequence given by $x_1=1$ and $x_{n+1}=x_n+\sqrt{x_n^2+1}$
negative_passages.docid: 14836
negative_passages.text: A polynomial sequence
negative_passages.docid: 88261
negative_passages.text: Convergence of a sequence in two different $L_p$ spaces
negative_passages.docid: 128975
negative_passages.text: Behavior of $\|f\|_p$ when $p$ is near the endpoint of $I$
negative_passages.docid: 113384
negative_passages.text: $\sum_{n\geq1} k_n x_n$ converges for every $x \in l_1$, then $\sup_{n\geq1} |k_n| < \infty$
negative_passages.docid: 29655
negative_passages.text: $L^p$ and $L^q$ space inclusion
negative_passages.docid: 42265
negative_passages.text: A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
negative_passages.docid: 38090
negative_passages.text: Partial sums of $nx^n$
negative_passages.docid: 110275
negative_passages.text: Let $p>0$. Show the $\lim_{n\to\infty}(a^n/n^p)$ is equal to:
negative_passages.docid: 122115
negative_passages.text: Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
negative_passages.docid: 115111
negative_passages.text: Limit of the sequence $nx_{n}$ where $x_{n+1} = \log (1 +x_{n})$
negative_passages.docid: 98762
negative_passages.text: $f_n(x) = x - x^n$ for $x\in [0,1]$. Does the sequence converge pointwise or uniformly on $[0,1]$?
negative_passages.docid: 13684
negative_passages.text: Find the values of $p$ for which $\sum_{n=2}^\infty \frac{1}{n(\ln n)^p}$ is convergent
negative_passages.docid: 65168
negative_passages.text: Proof of sequence inequality