Let $\kappa$ be an infinite cardinal and let $B$ be the random forcing for adding $\kappa$-many random reals.


**Question:** What are the elements of $B$. More precisely given a condition $p \in B$, what are the domain and the range of $p$, if there are any?. What does it mean "a coordinate of $p$"?.



Random real forcing
There are different ways of representing $B$. One possibility is to let $B$ consist of all closed subsets of $2^\kappa$ of positive measure; another possibility is to allow all positive Borel sets. Two conditions are equivalent if their symmetric difference has measure zero. 


Each basic clopen set has a finite set of coordinates. By ccc, each open set is almost the same as some open set that uses only countably many coordinates. So every closed/Borel set $p$ is equivalent to a set that uses only countably many coordinates. I guess that these are the "coordinates of $p$". 


