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Use the Cauchy-Schwarz inequality to prove $||x||_1 \leq \sqrt{n}||x||_2$

Awarded Sep 15, 2022 at 17:31

Let $f$ be integrable over $\mathbb{R}$. Show that the following four assertions are equivalent:

Awarded May 6, 2022 at 18:21

Let $F,G$ to be distribution. Is the product $FG$ also a distribution?

Awarded Mar 17, 2022 at 11:08

Let $E$ have finite outer measure. Prove that there exist a $G_{ \delta}$ set $G$ with $E \subseteq G$

Awarded Mar 9, 2022 at 22:17

Let $f$ be of bounded variation on $[a,b]$, and define $v(x) = f_{[a,x]}$. show $\int_a^b |f'|\leq TV(f).$

Awarded Jan 2, 2022 at 17:42

Let $\mathcal{F}$ be a $\sigma$-algebra and let $B \in \mathcal{F}$. Show that $\mathcal{G} = \{A \cap B: A \in \mathcal{F}\}$ is a $\sigma-$algebra.

Awarded Nov 23, 2021 at 16:16

Best strategy for a fair die game provided if its shows 1 you stop.

Awarded Sep 30, 2021 at 4:46

If $V$ is a vector space to itself, is the idempotent linear transformation, prove there is a basis such that is a diagonal matrix with all $0$ or $1$

Awarded Sep 16, 2021 at 12:55

Inner approximation by closed sets if $E$ is measurable

Awarded Sep 9, 2021 at 20:40

Let $W$ be a Wiener process. Which of the following define a Wiener process?

Awarded Mar 30, 2021 at 23:47

"There are exactly two values of $x$ for which $P(x)$ is true" formula using logical symbols

Awarded Feb 13, 2021 at 23:33

Are these functions of bounded variations?

Awarded Mar 6, 2020 at 4:20

Find the sigma algebra generated by the following sets

Awarded Jan 29, 2020 at 20:00

How to solve Inequality with factorials

Awarded Jan 26, 2020 at 20:20

Prove that $\sigma$-algebra of subsets of $\mathbb{R}$ of the form $(a,\infty)$ contains all the intervals.

Awarded Jan 18, 2020 at 3:40

sums and product of density functions are density?

Awarded Dec 23, 2019 at 8:40

prove that a partially ordered set of elements mn+1 has a chain of size m+1 or antichain of size n+1

Awarded Aug 30, 2019 at 6:40

Let $f$ be Lipschitz and $g$ be absolutely continuous. Show that the composition $f\circ g$ is absolutely continuous.

Awarded Jun 2, 2019 at 19:00

If $n\mid m$ prove that the canonical surjection $\pi: \mathbb Z_m \rightarrow \mathbb Z_n$ is also surjective on units

Awarded Feb 13, 2019 at 18:40

Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$

Awarded Feb 5, 2019 at 3:30

Translate of $F_{\sigma}$, $G_{\delta}$ and a set of measure $0$

Awarded Mar 8, 2018 at 4:14

Let $f$ be a bounded measurable function on $E$. Show that there are sequences of simple functions converging uniformly on $E$.

Awarded Jan 1, 2018 at 10:19

$3 \times 3$ matrices are similar if and only if they have the same characteristic and minimal polynomial

Awarded Dec 25, 2017 at 1:55

Prove the $n$th Fibonacci number is the integer closest to $\frac{1}{\sqrt{5}}\left( \frac{1 + \sqrt{5}}{2} \right)^n$

Awarded Oct 4, 2017 at 19:14

How to fill my mathematical gaps?

Awarded Sep 1, 2017 at 0:02

Probability of secretary making 4 or more errors on a page [closed]

Awarded Jan 26, 2017 at 11:39

Prove every prime ideal of a ring is a radical ideal.

Awarded Nov 13, 2016 at 20:56

Show that the Cantor set is nowhere dense

Awarded Sep 29, 2016 at 0:46

Upper Triangular Block Matrix Determinant by induction

Awarded Aug 15, 2016 at 0:34

Proof the Legendre polynomial $P_n$ has $n$ distinct real zeros

Awarded Feb 2, 2015 at 9:30

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