It is trivially true but maybe worth noting that the converse is also true - if there exists such an f, then Y is σ(X)-measurable.
This and the question asked are theorem 20.1(ii) in Billingsley's Probability and Measure, 3rd edition.
|
2 | added 109 characters in body | ||
|
|
||||
|
|
1 |
|
||
|
It is trivially true but maybe worth noting that the converse is also true - if there exists such an f, then Y is σ(X)-measurable. |
||||
