query: $X\stackrel{d}{=}E[X|\mathcal{G}]\implies X=E[X|\mathcal{G}]$ a.s.
positive_passages.docid: 156901
positive_passages.text: Showing that $X\sim E[X\mid\mathcal{G}]$ implies $X=E[X\mid\mathcal{G}]$ almost surely
negative_passages.docid: 132532
negative_passages.text: Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
negative_passages.docid: 106799
negative_passages.text: Proof Verification: Converse of Intermediate Value Theorem
negative_passages.docid: 86977
negative_passages.text: If $\cup \mathcal{F}=A$ then $A \in \mathcal{F}$. Prove that $A$ has exactly one element.
negative_passages.docid: 67709
negative_passages.text: Stuck with proof for $\forall A\forall B(\mathcal{P}(A)\cup\mathcal{P}(B)=\mathcal{P}(A\cup B)\rightarrow A\subseteq B \vee B\subseteq A)$
negative_passages.docid: 121465
negative_passages.text: $R[x]$ has a subring isomorphic to $R$.
negative_passages.docid: 149362
negative_passages.text: Prove that $ \mathbb{E}[XY] - \mathbb{E}[X] \mathbb{E}[Y] = \int_{- \infty}^\infty \int_{- \infty}^\infty (F(x,y)-F_X(x) F_Y(y)) \,dx\,dy,$
negative_passages.docid: 2907
negative_passages.text: How do I show that $x$ is a root of $p(x)$ in $F[x]/\langle p(x)\rangle$?
negative_passages.docid: 23946
negative_passages.text: Prove the definitions of $e$ to be equivalent
negative_passages.docid: 140790
negative_passages.text: Prove that $E(X) = \int_{0}^{\infty} P(X>x)\,dx = \int_{0}^{\infty} (1-F_X(x))\,dx$.
negative_passages.docid: 153634
negative_passages.text: A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.
negative_passages.docid: 39943
negative_passages.text: Proving $\mathrm e <3$
negative_passages.docid: 118049
negative_passages.text: Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
negative_passages.docid: 130537
negative_passages.text: Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
negative_passages.docid: 19599
negative_passages.text: $ d(x_n,y_n) \to d(x,y)$ if $x_n\to x$ and $y_n \to y$
negative_passages.docid: 135694
negative_passages.text: Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
negative_passages.docid: 58562
negative_passages.text: How can we prove that $D(f)\backsimeq\operatorname{Spec} A_f$?