The metric measure boundary of spaces with Ricci curvature bounded below

We solve a conjecture raised by Kapovitch, Lytchak and Petrunin in [KLP21] by showing that the metric measure boundary is vanishing on any RCD(K,N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\textrm{RCD}\,}}(K,N)$$\end{document} space (X,d,HN)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(X,{\textsf{d}},{\mathscr {H}}^N)$$\end{document} without boundary. Our result, combined with [KLP21], settles an open question about the existence of infinite geodesics on Alexandrov spaces without boundary raised by Perelman and Petrunin in 1996.