There is some occasion where it may be useful to introduce a notation for the notion of an aggregation of unordered but not necessarily distinct elements; e.g., consider the theory of probability.
However, a standard set notation, although implying the lack of order, also implies distinctness, which is not desired here; a standard tuple notation, on the other hand, implies order although implied is also the lack of distinctness. It seems that (due to my shallow observations) authors in probability theory take care of this little issue only out of discretion.
I would like to, therefore, know if there is any established standard notation, perhaps in set theory or logic, which overcomes the issue under consideration. Thanks.