 Null set

A measurable set $N$ is a null set for a measure $\mu$ when $\mu (N)=0$. A property holds almost everywhere when its exceptions lie in a null set. With a complete measure, every subset of a null set is measurable and is itself a null set.

A null set, also known as an empty set, is a fundamental concept in set theory. It is defined as a set that contains no elements. The null set is typically denoted by the symbol ∅ or by using curly braces, such as {}. Some key points about the null set include: 1. **Unique Set**: There is only one null set, which is unique, meaning that any two null sets are considered to be the same set.