definition of measurable subspace
Topics
About: measurable space
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
Starting Context
- The reader knows a definition of measurable space.
- The reader knows a definition of subspace \(\sigma\)-algebra of subset of measurable space.
Target Context
- The reader will have a definition of measurable subspace.
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:
\( (M', A')\): \(\in \{\text{ the measurable spaces }\}\)
\( M\): \(\subseteq M'\)
\( A\): \(= \text{ the subspace } \sigma\text{ -algebra of the subset, } M \text{, of } (M', A')\)
\(*(M, A)\): \(\in \{\text{ the measurable spaces }\}\)
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Conditions:
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2: Natural Language Description
For any measurable space, \((M', A')\), any subset, \(M \subseteq M'\), and the subspace \(\sigma\)-algebra of the subset, \(M\), of \((M', A')\), \(A\), the measurable space, \((M, A)\)
