Imagine there is a continuum of firms in the economy. Each draws its productivity from the same stochastic process. The stochastic process has unbounded support. The only securities in the economy are the firm's shares.
The claim is that markets are incomplete because the cardinality of the states of the world is $\aleph_2$ and the cardinality of the securities is $\aleph_1$.
However one could also argue that since there is a continuum of firms, the strong law of large numbers applies and one knows exactly the proportion of firms that will get each shock, hence there is no risk (and markets would be complete)
Which of the two statements is correct?