Index of notation/B
From Maths
Expression | Status | Meanings | See also |
---|---|---|---|
[ilmath]\mathcal{B} [/ilmath] | current | The Borel sigma-algebra of the real line, sometimes denoted [ilmath]\mathcal{B}(\mathbb{R})[/ilmath]. [ilmath]\mathcal{B}(X)[/ilmath] denotes the Borel sigma-algebra generated by a topology (on) [ilmath]X[/ilmath]. | [ilmath]\mathcal{B}(\cdot)[/ilmath] |
[ilmath]\mathcal{B}(\cdot)[/ilmath] | current | Denotes the Borel sigma-algebra generated by [ilmath]\cdot[/ilmath]. Here the "[ilmath]\cdot[/ilmath]" is any topological space, for a topology [ilmath](X,\mathcal{J})[/ilmath] we usually still write [ilmath]\mathcal{B}(X)[/ilmath] however if dealing with multiple topologies on [ilmath]X[/ilmath] writing [ilmath]\mathcal{B}(\mathcal{J})[/ilmath] is okay. If the topology is the real line with the usual (euclidean) topology, we simply write [ilmath]\mathcal{B} [/ilmath] | [ilmath]\mathcal{B} [/ilmath] |