The cokernel of a random p-adic matrix can be used to study the distribution of objects that arise naturally in number theory. For example, Cohen and Lenstra suggested a conjectural distribution of the p-parts of the ideal class groups of imaginary quadratic fields. Friedman and Washington proved that the distribution of the cokernel of a random p-adic matrix is the same as the Cohen–Lenstra distribution. Recently, Wood generalized the result of Friedman–Washington by considering a far more general class of measure on p-adic matrices. In this talk, we explain a further generalization of Wood’s work. This is joint work with Dong Yeap Kang and Jungin Lee.