My mathematical statistics book denotes $\sigma$-field as following:
Let $\Bbb B$ be the collection of subsets of $\Bbb C$ where $\Bbb C$ denotes sample space which is the collection of all possible events. Then $\Bbb B$ is $\sigma$-field if
(1) $\emptyset \in \Bbb B$ and $\exists b \in \Bbb B$ s.t. $\emptyset \subset b$
(2) $C \in \Bbb B \Rightarrow C^c\in \Bbb B $ where $C \in \Bbb C$
(3) $\{C_1, C_2, C_3..\} \in \Bbb B \Rightarrow \cup_{i=1}^{\infty}C_i \in \Bbb B$ where $\{C_1, C_2, C_3..\}$ is countable collection of subsets of $\Bbb C$
Is this field a specific example of Borel Field? or this field is eqaully defined with Borel Field?