Intergenerational equity: sup,inf, lim sup,and lim inf

We study the problem of intergenerational equity for utility streams and a countable set of agents. A numerical social welfare function is invariant to ordinal transformation, satisfies a weak monotonicity condition, and an invariance with respect to concatenation of utility streams if and only if it is either the sup, inf, lim sup, or lim inf. I would like to thank Federico Echenique, Marc Fleurbaey, and Toyotaka Sakai for discussions on intergenerational equity. Two anonymous referees and the Associate Editor also provided very useful comments. All errors are my own.