I would expect any way to get a truly fair sample from a truly fair sample would necessarily result in a truly fair sample. I can't imagine how it could possibly not.
In the first instance, every second we get a 'truly fair' random sample from all the messages in that second.
Going from there to eg a 'truly fair' random sample from all the messages in a minute is not trivial. And it's not even possible just from the samples, without auxiliary information.
In the first instance, every second we get a 'truly fair' random sample from all the messages in that second.
Going from there to eg a 'truly fair' random sample from all the messages in a minute is not trivial. And it's not even possible just from the samples, without auxiliary information.