I am a self-taught learner, have no formal training in measure theory.
After plenty of readings, I'm assuming that the Borel field appears to contain almost every possible collection of intervals that can be imagined.
I came across the $\mathcal B[0,∞)\times \mathcal B(\Bbb R \setminus \{0\})$, say $\mathscr B$, notation in Levy measures.
If we have something for e.g. $A = \{a_1,b_1,c_1\}, B = \{a_2,b_2,c_2\}$, we can easily see the Cartesian product. Then, in various combinations, a total of nine ordered pairs can be drawn.
I have searched for $R \setminus \{0\}$ meaning, which says $(−∞,0)\cup(0,∞)$.
If I further see $\mathscr B$ in terms of $A \times B$, but then because of $\mathcal B (R \setminus \{0\})$, I am unable to see the combination of pairs as in $A \times B$.
For on the cartesian plane, I tried to see $\mathcal B[0, ∞)$ the +ve real line of the $x-$axis and $\mathcal B((−∞,0)\cup(0,∞))$ is the y-axis's real line excluding $\{0\}$. But I still can't work out how to make disjoint sets from $\mathcal B[0, ∞) × \mathcal B (R\setminus\{0\})$.
Briefly, I am unable to reckon the idea behind $\mathscr B$.
Please use an example or visualization to help me to understand.