A real valued function u defined in the upper half space \(R^ n_+\) is called Dirichlet finite if u is continuous, \(A\subset L^ n\) and \(\int_{R^ n_+}| \nabla u|^ ndm<\infty;\) locally finite Dirichlet functions are defined via the requirement \(\int_{D(x,M)}| \nabla u|^ ndm\leq B\) whenever \(x\in R^ n_+\) and D(x,M) is the hyperbolic ball in \(R^ n_+\) centered at x and radius M. Monotone functions in the latter class are shown to be uniformly continuous in the hyperbolic metric of \(R^ n_+\). Also in this class the function \(e^ u\) satisfies a Harnack type inequality. Boundary behavior of monotone Dirichlet finite functions u is studied: (1) u has an angular limit at each point of \(\partial R^ n_+\setminus E\) where E is a set of zero n-capacity, (2) a variant of the Iversen-Tsuji theorem on the limit values along the boundary. Isolated singularities of monotone \(A\subset L^ n\) functions are also considered.