Metric mean dimension of irregular sets for maps with shadowing

We study the metric mean dimension of phi-irregular set $ I_{\Phi }(f) $ I phi(f) in dynamical systems with the shadowing property. In particular, we prove that for dynamical systems with the shadowing property containing a chain recurrent class Y, the values of topological entropy together with the values of lower and upper metric mean dimension of the set $ I_{\Phi }(f)\cap B(Y,\varepsilon )\cap CR(f) $ I phi(f)boolean AND B(Y,epsilon)boolean AND CR(f) are bounded from below by the respective values for class Y.