I am watching a video on sufficient statistics here.
In the video, the sufficient statistics is defined as follows. I am puzzled by the part in the red box. I know it is describing some trivial situation, but I don't quite understand what this statement is talking about and how it is related to the definition of sufficient statistics. Thank you!
This screen capture is at about 5:00 of the video.
Like it said, a null set is just a set where $P_{\theta} (A)=0$ for all $\theta$. For a specific example, consider the uniform probability on $[0,1]$. Then the set $\{.5\}$ is a null set, as $P(.5)=0$.