query: In probability theory what does the notation $\int_{\Omega} X(\omega) P(d\omega)$ mean?
positive_passages.docid: 23843
positive_passages.text: Abstract Integration in Elementary Probability Theory
negative_passages.docid: 44285
negative_passages.text: What does this notation mean? F|U
negative_passages.docid: 84413
negative_passages.text: Why is $\int_{-\infty}^\infty |g(x)|\,dx = \int_0^\infty \mu(\{x : |g(x)| \ge t\})\,dt$ true?
negative_passages.docid: 131251
negative_passages.text: Picking a $\delta$ for a convenient $\varepsilon$?
negative_passages.docid: 138729
negative_passages.text: What happens when $\lvert\omega\rvert =1$?
negative_passages.docid: 60617
negative_passages.text: How compute $\lim_{p\rightarrow 0} \|f\|_p$ in a probability space?
negative_passages.docid: 76561
negative_passages.text: Domain of ProbabilityDistributions
negative_passages.docid: 67394
negative_passages.text: How to interpret $\mathbb{P}(B|A)$ when $\mathbb{P}(A) = 0$
negative_passages.docid: 89185
negative_passages.text: The notation for partial derivatives
negative_passages.docid: 134922
negative_passages.text: Which notation and why: $\text{P}()$, $\Pr()$, $\text{Prob}()$, or $\mathbb{P}()$
negative_passages.docid: 35454
negative_passages.text: Is it correct to write $\Bbb E[X]$ or $\Bbb E_{\theta}[X]$?
negative_passages.docid: 81160
negative_passages.text: What does the notation $\Gamma \vDash \phi$ mean (in Mathematical Logic)?
negative_passages.docid: 128600
negative_passages.text: How to evaluate this integral$\int_{-\infty}^\infty\dfrac{\omega^\alpha e^{i\omega t}}{(\omega_0^2-\omega^2)^{2}+4(\zeta\omega_0\omega)^2}\,d\omega$
negative_passages.docid: 86623
negative_passages.text: Why is $B^TB+\lambda\Omega$ positive definite?
negative_passages.docid: 71725
negative_passages.text: $\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ notation
negative_passages.docid: 85
negative_passages.text: Difference between $\Delta$, $d$ and $\delta$
negative_passages.docid: 34918
negative_passages.text: Difference between $R^\infty$ and $R^\omega$