All Questions
Tagged with borel-sets pr.probability
8 questions
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Definition of "interval of continuity" for function defined on sets
At the beginning of Chapter 8 of Kubilius's Probabilistic Methods in the Theory of Numbers, the author defines $Q=Q(E)$ to be a completely additive nonnegative function defined for all Borel subsets $...
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Getting almost certainty from uncountably many low-probability events
Let $(\Omega,\Sigma,\mathbb{P})$ be a complete probability space, $B\subseteq X$ be a non-empty Borel subset of a polish space $X$, $A$ be an uncountable indexing set, and $\{X_{\alpha,n}\}_{a \in A, ...
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1
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Countable convergence-determining class for weak convergence of probability measures
Suppose that $E$ is a Polish space.
Portmanteau theorem asserts that a sequence $(\mu_n)$ of Borel probability measures weakly converges to a Borel probability measure $\mu$ (shortly, $\mu_n\overset{...
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Explicit examples of (probability) measures on $\prod \mathbb{R}$
Let $\prod_{n \in \mathbb{N}} \mathbb{R}$ be equipped with the Tikhonov product of the Euclidean topologies on $\mathbb{R}$ and let $B$ the corresponding Borel $\sigma$-algebra. What is are some ...
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Regular measure in finite Borel sets [closed]
I have a question concerning
these lecture notes, https://www.math.leidenuniv.nl/~vangaans/jancol1.pdf
In the proof of the proposition 2.3 (page 3), there are two steps:
1) define the family $\...
- 111
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1
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Absolute continuity of probabilities on Polish spaces and open sets. [closed]
On a polish space $\mathcal{X}$ i consider two Borel probabilities $P$ and $Q$ such that for any open set $E$ of $\mathcal{X}$ we have : $P(E) =0$ implies $Q(E)=0$. Does this imply that $Q$ is ...
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Is the set of the absolutely continuous functions a Borel set of the space of the continuous functions?
Does anyone knows whether the set of the absolutely continous functions $F :[0,1]\to \mathbb{R}^d$ of the form $$F(t)= a + \int_0^tf(s) ds$$ where $f$ is an integrable function is a Borel set of the ...
- 125
6
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10
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Best introduction to probability spaces, convergence, spectral analysis
I'm not sure if this stuff all falls under what most would just term "probability", but I'm researching applied macroeconomics and need to get a handle on the following concepts ASAP:
probability ...
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