Let denote a measure space and let for . The sequence converges to in measure if for any . Furthermore, the sequence is Cauchy in measure if for every as 
- If in measure and in measure, then in measure.
- If in measure and in measure, then in measure if this is a finite measure space. 
Relation to other types of Convergence
- If in then in measure 
- If in measure, then there exists a subsequence such that almost everywhere.
- If and measurable s.t. almost everywhere Then in measure.
- ↑ 1.0 1.1 1.2 Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, second edition, §2.4
- ↑ 2.0 2.1 Craig, Katy. MATH 201A HW 8. UC Santa Barbara, Fall 2020.
- ↑ Craig, Katy. MATH 201A Lecture 18. UC Santa Barbara, Fall 2020.