# Tagged Questions

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### Not countable generated sigma field

I need to show that $F=(A \in \Omega$| A countable or co-countable) with $\Omega$=(0,1] is not countable generated. I have started supposing that F is countable generated and I have a hont that tell ...
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### Borel measurable function

I'm struggling on the following question from a past paper: Suppose that $f:\mathbb{R}\rightarrow \mathbb{R}$ is a Borel measurable function and let $h:\mathbb{R}^2\rightarrow \mathbb{R}$ be defined ...
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### If $f:\mathbb{R}\longrightarrow \mathbb{R}$ be Borel measurable and $\lambda$ is Lebesgue measurable on $\mathbb{R}$, then which case is establish [on hold]

If $f:\mathbb{R}\longrightarrow \mathbb{R}$ is Borel measurable and $\lambda$ is the Lebesgue measure on $\mathbb{R}$, then which case is establish? the function $g(x,y)=f(x+y)$ on $\mathbb{R}^{2}$, ...
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### Measure Theory - condition for Integrability

A question from my homework: Let $f:X\to [0,\infty)$ be a measurable function w.r.t to the Lebesgue measure and the Borel Sigma Algebra. Show that $\int_Xf(x)\,d\mu < \infty$ iff ...
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### Gaussian random variable in $\mathbb{R}^n$ question
Let $X=(X_1,...,X_n)$ is a Gaussian random variable in $\mathbb{R}^n$ with mean $\mu$ and covariance matrix $V$. I want to show that we can write $X_2$ in the form $X_2 = aX_1 + Z$, where $Z$ is ...
If $(X_n: n\in \mathbb{N}), X$ are a sequence of random variables in $\mathbb{R}$, I wish to show that $X_n \to X$ weakly if and only if $X_n \to X$ in distribution. By 'converging weakly' I mean that ...