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Suppose (X,\omega) is a compact K\"ahler manifold. In the present work wepropose a simple construction for weak geodesic rays in the space of K\"ahlermetrics that seems to be tied together with properties of the classE(X,\omega). As an application of our construction, we prove a characterizationof E(X,\omega) in terms of envelopes.

Weak geodesic rays in the space of K\"ahler potentials and the class E(X,\omega)