# Borel sigma-algebra [on hold]

Borel $$\sigma$$-field $$\mathcal{B}(C)$$

From Wikipidia, a Borel set is any set in a topological space that can be formed from $$\mathbf open$$ $$\mathbf sets$$ (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement.

Can we take a Borel $$\sigma$$-field $$\mathcal{B}(C)$$ , where C represents a Banach space of real-valued continuous functions $$\omega$$ on [0,1] with $$\omega(0)=0.$$

Introduction to Stochastic Integration by Hui-Hsiung Kuo, page 24.

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## put on hold as unclear what you're asking by Kavi Rama Murthy, Brahadeesh, José Carlos Santos, Rebellos, DRFDec 7 at 14:10

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• In a Banach space, the norm defines a topology, so we then can get a $\sigma$-field from the open sets in the topology. – herb steinberg Dec 7 at 4:14
• I got confused about the elements of C, and your explanation makes it dawned on me. Thanks! – Peter Van Dec 7 at 12:48