In this note we show that locally p-admissible measures on R necessarily come from local Muckenhoupt A(p) weights. In the proof we employ the corresponding characterization of global p-admissible measures on R in terms of global A(p) weights due to Bjorn, Buckley and Keith, together with tools from analysis in metric spaces, more specifically preservation of the doubling condition and Poincare inequalities under flattening, due to Durand-Cartagena and Li. As a consequence, the class of locally p-admissible weights on R is invariant under addition and satisfies the lattice property. We also show that measures that are p-admissible on an interval can be partially extended by periodical reflections to global p-admissible measures. Surprisingly, the p-admissibility has to hold on a larger interval than the reflected one, and an example shows that this is necessary. (C) 2019 Elsevier Inc. All rights reserved.