definition of independent indexed set of events of probability space
Topics
About: measure space
The table of contents of this article
Starting Context
- The reader knows a definition of probability space.
- The reader knows a definition of indexed set.
Target Context
- The reader will have a definition of independent indexed set of events of probability space.
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:
\( (M, A, \mu)\): \(\in \{\text{ the probability spaces }\}\)
\( J\): \(\in \{\text{ the possibly uncountable index sets }\}\)
\(*\{a_j \in A\}_{j \in J}\): \(\in \{\text{ the indexed sets }\}\)
//
Conditions:
\(\forall J^` \in \{\text{ the finite subsets of } J\} (\mu (\cap_{j \in J^`} a_j) = \prod_{j \in J^`} \mu (a_j))\)
//
