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I sense that, I did not understand the concept of premeasure well. I know the conditions which it satisfies but conceptually it is not clear in my mind.

For instance, I could clearly think about the outer measure (In my mind, the outer measure of an arbitrary set $E$ is defined on a grid, and it is the infimum of the sets of grids including $E$).

The definitions of premeasure and outer measure are somewhat related and I sense premeasure is a simple concept, however I do not get it. Would someone clarify this? Thanks!

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