POSITIVE ELECTRODE ACTIVE MATERIAL FOR NON-AQUEOUS ELECTROLYTE SECONDARY BATTERY, METHOD FOR PRODUCTION OF POSITIVE ELECTRODE ACTIVE MATERIAL FOR NON-AQUEOUS ELECTROLYTE SECONDARY BATTERY, POSITIVE ELECTRODE FOR NON-AQUEOUS ELECTROLYTE SECONDARY BATTERY, AND NON-AQUEOUS ELECTROLYTE SECONDARY BATTERY

A positive electrode active material for non-aqueous electrolyte secondary battery is improved so that a reaction between the positive electrode active material and a non-aqueous electrolyte is restricted in a case where charging voltage is increased. In a non-aqueous electrolyte secondary battery including a positive electrode 1, a negative electrode 2 and a non-aqueous electrolyte, a positive electrode active material wherein a particle of at least one compound selected from Er hydroxide, Er oxyhydroxide, Yb hydroxide, Yb oxyhydroxide, Tb hydroxide, Tb oxyhydroxide, Dy hydroxide, Dy oxyhydroxide, Ho hydroxide, Ho oxyhydroxide, Tm hydroxide, Tm oxyhydroxide, Lu hydroxide, and Lu oxyhydroxide is dispersed and adhered on a surface of a positive electrode active material particle containing Li is used.