Definition (h-interval)

Intervals of the following form:

• $(a,b]:-\infty\le a<b<\infty$
• $(a,\infty): -\infty\le a<b$
• $\emptyset$

are called h-intervals.

Definition (Collection of all finite disjoint h-intervals)

Let $\mathscr{A}$ be the collection of all finite disjoint h-intervals.

• $\mathscr{A}$ is an Algebra
• The Smallest σ-algebra containing $\mathscr{A}$ is the Borel σ-algebra