# Kuba Helsztyński

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bio website location Warsaw, Poland age 22 member for 1 year, 7 months seen Jan 31 at 20:24 profile views 363

 5 Counterexample for $(p\rightarrow q) \longleftrightarrow (!q \rightarrow\mathord !p)$ 4 Show $\lim\limits_{n\to\infty} \sqrt[n]{n^e+e^n}=e$ 3 $\mu(E\setminus (E+x))=0$ for all $x\in\mathbb{R}$. Prove that $\mu(E)=0$ or $\mu(\mathbb{R}\setminus E)=0$ 3 Equivalent metrics determine the same topology 2 Is a linear map of norm $1$ always an isometry?

# 1,026 Reputation

 +5 $\mu(E\setminus (E+x))=0$ for all $x\in\mathbb{R}$. Prove that $\mu(E)=0$ or $\mu(\mathbb{R}\setminus E)=0$ +10 $\mu(E\setminus (E+x))=0$ for all $x\in\mathbb{R}$. Prove that $\mu(E)=0$ or $\mu(\mathbb{R}\setminus E)=0$ +10 Lebesgue integrable function when integrated on a set is less that $\epsilon$ +2 What does it mean by $\mathcal{F}$-measurable?

# 12 Questions

 6 $\mu(E\setminus (E+x))=0$ for all $x\in\mathbb{R}$. Prove that $\mu(E)=0$ or $\mu(\mathbb{R}\setminus E)=0$ 4 Prove that $\frac{1}{2h}\int_a^b\mu(A\cap(x-h,x+h))\,\text{d}x\le \mu(A)$ 4 Do probability measures have to be the same if they agree on a generator of Borel $\sigma$–algebra $\mathcal{B}(\mathbb{R})$? 3 Favourable modification of “Double or Nothing” 3 Show there is no measure on $\mathbb{N}$ such that $\mu(\{0,k,2k,\ldots\})=\frac{1}{k}$ for all $k\ge 1$

# 28 Tags

 8 homework × 10 4 general-topology × 2 6 logic × 2 4 limits 5 measure-theory × 10 3 probability × 4 5 metric-spaces × 2 2 probability-theory × 7 5 propositional-calculus 2 real-analysis × 2

# 2 Accounts

 Mathematics 1,026 rep 1615 Academia 101 rep 1