definition of \(\sigma\)-finite measure over \(\sigma\)-algebra of set
Topics
About: measure space
The table of contents of this article
Starting Context
- The reader knows a definition of measure over \(\sigma\)-algebra of set.
Target Context
- The reader will have a definition of \(\sigma\)-finite measure over \(\sigma\)-algebra of set.
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:
\( (M, A)\): \(\in \{ \text{ the measurable spaces }\}\)
\(*\mu\): \(\in \{\text{ the measures over } A\}\)
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Conditions:
\(\exists s: \mathbb{N} \to A (\cup_{j \in \mathbb{N}} s (j) = M \land \forall j \in \mathbb{N} (\mu (s (j)) \lt \infty))\)
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