Index of notation/B

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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]