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Let $L_N = L_{MBM}(X_1,..., X_N; Y_1,..., Y_N)$ be the minimum length of abipartite matching between two sets of points in $\mathbf{R}^d$, where$X_1,..., X_N,...$ and $Y_1,..., Y_N,...$ are random points independently anduniformly distributed in $[0,1]^d$. We prove that for $d \ge 3$,$L_N/N^{1-1/d}$ converges with probability one to a constant $\beta_{MBM}(d)>0$as $N\to \infty $.

Almost Sure Convergence of the Minimum Bipartite Matching Functional in Euclidean Space