Generators of the real Borel algebra (incomplete)

Dependencies: (incomplete)

1. Borel algebra

Let $F$ be the set of all open sets of $\mathbb{R}$ of the form $(-\infty, a)$. Then $\mathcal{B}(\mathbb{R}) = \sigma(F)$.

Let $G$ be the set of all sets of $\mathbb{R}$ of the form $(-\infty, a]$. Then $\mathcal{B}(\mathbb{R}) = \sigma(G)$.

(Proof needed)

Dependency for:

1. Random variable
2. Independence of random variables (incomplete)

Info:

• Depth: 4
• Number of transitive dependencies: 5

Transitive dependencies:

1. /analysis/topological-space
2. /sets-and-relations/countable-set
3. σ-algebra
4. Generated σ-algebra
5. Borel algebra