噪声作为$σ$ -域的布尔代数
Noise as a Boolean algebra of $σ$-fields
摘要：
噪声是从整环的布尔代数到$σ$ -域的格的一种同态。撇开同态，我们研究它的图像，一个$σ$ -域的布尔代数。$σ$ -域的这种布尔代数的最大扩张总是定义良好的，是完备的布尔代数当且仅当噪声是经典的，这回答了J. Feldman的一个老问题。
英文摘要：
A noise is a kind of homomorphism from a Boolean algebra of domains to the lattice of $σ$-fields. Leaving aside the homomorphism we examine its image, a Boolean algebra of $σ$-fields. The largest extension of such Boolean algebra of $σ$-fields, being well-defined always, is a complete Boolean algebra if and only if the noise is classical, which answers an old question of J. Feldman.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
