Positive Electrode Active Substance for All Solid-State Lithium Secondary Battery

A positive electrode active substance for an all solid-state lithium secondary battery, wherein the surface of the present core particles composed of a lithium metal composite oxide having a layered structure containing Li, M element, where M includes at least one element or a combination of two or more elements selected from the group consisting of Ni, Co, Mn, and Al, and O is coated with an amorphous compound containing Li, A, where A represents one element or a combination of two or more elements selected from the group consisting of Ti, Zr, Ta, Nb, Zn, W, and Al, and O, and wherein the D50 is 0.5 to 11 μm, the value of (|mode diameter−D50|/mode diameter)×100 is 0 to 25%, the value of (|mode diameter−D10|/mode diameter)×100) is 20 to 58%, and the value of average primary particle diameter/D50 is 0.01 to 0.99.