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Jun 7, 2018 at 9:06 comment added psarka @whuber Agreed, edited the answer to incorporate your remark.
Jun 7, 2018 at 9:05 history edited psarka CC BY-SA 4.0
Expanded the answer to incorporate Whuber's remark
Jun 6, 2018 at 20:54 comment added whuber It won't work to "assign equal mass to all the points in $\Omega$" because not all samples possibly can have equal probability. For taking samples of size $n$ (without replication), consider letting $\Omega$ be the set of all $n$-subsets of the population and give it the discrete sigma algebra. You don't have to specify a probability measure: that will be determined by how the samples are selected.
Jun 6, 2018 at 20:43 history answered psarka CC BY-SA 4.0