921: Measurable Subspace

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definition of measurable subspace

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Topics

About: measurable space

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Natural Language Description

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Starting Context

• The reader knows a definition of measurable space.
• The reader knows a definition of subspace $\sigma$-algebra of subset of measurable space.

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Target Context

• The reader will have a definition of measurable subspace.

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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.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$(M^{\prime },A^{\prime })$: $\in \{\text{ the measurable spaces }\}$
$M$: $\subseteq M^{\prime }$
$A$: $=\text{ the subspace }\sigma \text{ -algebra of the subset, }M\text{, of }(M^{\prime },A^{\prime })$
$\ast (M,A)$: $\in \{\text{ the measurable spaces }\}$
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Conditions:
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2: Natural Language Description

For any measurable space, $(M^{\prime },A^{\prime })$, any subset, $M\subseteq M^{\prime }$, and the subspace $\sigma$-algebra of the subset, $M$, of $(M^{\prime },A^{\prime })$, $A$, the measurable space, $(M,A)$

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References

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