query: Why $\mathscr{B}(\mathbb{R}) \times\mathscr{B}(\mathbb{R})$ is not a $\sigma$-algebra?
positive_passages.docid: 147486
positive_passages.text: Cartesian product of two $\sigma$-algebras is generally not a $\sigma$-algebra?
negative_passages.docid: 44685
negative_passages.text: Inner product on $C(\mathbb R)$
negative_passages.docid: 62711
negative_passages.text: Canonical map $R/(I\cap J)\rightarrow R/I\times _{R/(I+J)} R/J$ is an isomorphism
negative_passages.docid: 76048
negative_passages.text: Why does $PSL(2,\mathbb C)\cong PGL(2,\mathbb C)$ but $PSL(2,\mathbb R) \not\cong PGL(2,\mathbb R)$?
negative_passages.docid: 2458
negative_passages.text: Multiplicative group $(\mathbb R^*, ×)$ is group but $(\mathbb R, ×)$ is not group, why?
negative_passages.docid: 24561
negative_passages.text: $\mathbb S_n$ as semidirect product
negative_passages.docid: 129704
negative_passages.text: Why is the inclusion of the tensor product of the duals into the dual of the tensor product not an isomorphism?
negative_passages.docid: 29637
negative_passages.text: $\sigma$-algebra of sets that are both $G_\delta$ and $F_\sigma$
negative_passages.docid: 120442
negative_passages.text: Prove Borel sigma-algebra translation invariant
negative_passages.docid: 36131
negative_passages.text: $\sigma$-algebra vs. $\sigma$-field: is there any difference?
negative_passages.docid: 37904
negative_passages.text: Prove that the multiplicative groups $\mathbb{R} - \{0\}$ and $\mathbb{C} - \{0\}$ are not isomorphic.
negative_passages.docid: 81327
negative_passages.text: union of sigma algebra is sigma algebra
negative_passages.docid: 55157
negative_passages.text: $\sigma$-algebras on a countable set is generated by partitions of the set
negative_passages.docid: 108955
negative_passages.text: Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
negative_passages.docid: 4156
negative_passages.text: What is $\Bbb R^{\times}$? [unit group, ring to "times" power]
negative_passages.docid: 84148
negative_passages.text: Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$?
negative_passages.docid: 102284
negative_passages.text: $GL(n,\mathbb R)/SL(n,\mathbb R)$ is isomophic to $\mathbb R^\times$