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We study substitutions on countably infinite alphabet (withoutcompactification) as Borel dynamical systems. We construct stationary andnon-stationary generalized Bratteli-Vershik models for a class of suchsubstitutions, known as left determined. In this setting of Borel dynamics,using a stationary generalized Bratteli-Vershik model, we provide a new andcanonical construction of shift-invariant measures (both finite and infinite)for the associated class of subshifts.

Invariant measures and generalized Bratteli diagrams for substitutions on infinite alphabets