definition of measure subspace of measure space for measurable subset
Topics
About: measure space
The table of contents of this article
Starting Context
- The reader knows a definition of measure space.
- The reader knows a definition of subspace measure over subspace \(\sigma\)-algebra of measurable subset of measure space.
Target Context
- The reader will have a definition of measure subspace of measure space for measurable subset.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( (M', A', \mu')\): \(\in \{\text{ the measure spaces }\}\)
\( M\): \(\in A'\)
\( A\): \(= \text{ the subspace } \sigma \text{ -algebra of } M\)
\( \mu\): \(: A \to [0, + \infty]\), \(= \text{ the subspace measure }\)
\(*(M, A, \mu)\):
//
Conditions:
//
