In this work, we propose and investigate a new class of functions termed \((\mu ,\nu )-(\omega ,c)\) -pseudo almost automorphic functions. By employing tools from measure theory, we explore various fundamental properties of the associated \((\mu ,\nu )-(\omega , c)\) -ergodic components. Our study emphasizes key theoretical results within this newly developed framework, including completeness and composition theorems for the functional space of \((\mu ,\nu )-(\omega , c)\) -pseudo almost automorphic functions. Furthermore, we establish existence and uniqueness results for \((\mu ,\nu )-(\omega ,c)\) -pseudo almost automorphic solutions to a Lasota–Wazewska-type equation with two measures and mixed delays, where the coefficients themselves belong to this new functional class.
