Convergence in Measure
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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.
- Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, second edition, §2.4
- Craig, Katy. MATH 201A HW 8. UC Santa Barbara, Fall 2020.
- Craig, Katy. MATH 201A Lecture 18. UC Santa Barbara, Fall 2020.