In this article, the authors completely answer an open question, presented in Tao et al. [A bridge connecting Lebesgue and Morrey spaces via Riesz norms. Banach J Math Anal. 2021;15(1):20], showing that Riesz–Morrey space is truly a new larger than particular with critical index. Indeed, just real interpolation of for suitable indices. Moreover, further show aforementioned inclusion also proper...