Sub-probability measure

In the mathematical theory of probability and measure, a sub-probability measure is a measure that is closely related to probability measures.

While probability measures always assign the value 1 to the underlying set, sub-probability measures assign a value lesser than or equal to 1 to the underlying set.

is called a sub-probability measure if

{\displaystyle {\text{probability}}\implies {\text{sub-probability}}\implies {\text{finite}}\implies \sigma {\text{-finite}}}

So every probability measure is a sub-probability measure, but the converse is not true.

Also every sub-probability measure is a finite measure and a σ-finite measure, but the converse is again not true.