"Compactness in size" in functional spaces

In Chapter 4.9 of the book "Measures of non-compactors and condensation operators" (Vol. 55 of the Operator Theory: Advances and Applications), the authors mention the property "compactness in measure". They say

here compactness as It means compactness in the normed space. $ S $ Of all measurable finite functions, almost everywhere. $ x $, equipped with the standard

$$ || x || = inf_ {x> 0} {s + text {month} {t ,: , | x (t) | geq s } } $$

Where "$ text {month} , D $"means the measure of the set $ D $.

My questions are: Does this property have other names? And there are good sources in English that mention it?

The only sources I can find that use it are the documents of N. A. Erzakova, not all of them have been translated into English, and possibly a Russian article by P. P. Zabreiko.