# Pre-measure on a semi-ring

From Maths

**Stub grade: A***

This page is a stub

This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:

Needs fleshing out urgently. Follows the doctrine of measure theory

## Definition

As per the *doctrine*, a pre-measure on this site refers to measure on a ring of sets. A *pre-measure on a semi-ring of sets* is a precursor to a pre-measure. We can uniquely extend a pre-measure on a semi-ring to a pre-measure.

We then extend the pre-measure to an outer measure and go from there. This simplifies obtaining a measure as we can "go through" a pre-measure to get there, so we need only show a pre-measure on a semi-ring can be extended to a pre-measure.