Positive active material for lithium secondary battery, method for production thereof, electrode for lithium secondary battery and lithium secondary battery

The positive active material for a lithium secondary battery includes a lithium transition metal composite oxide having an ±-NaFeO 2 -type crystal structure and represented by the composition formula of Li 1+± Me 1-± O 2 (Me is a transition metal including Co, Ni and Mn and ± > 0). The positive active material contains Na in an amount of no less than 1900 ppm and no more than 8000 ppm, and has a 50% particle size (D50) of 5 µm or less in particle size distribution measurement. There is provided a method for production of the positive active material, wherein a precursor for synthesis of the lithium transition metal composite oxide is a hydroxide of a transition metal including Co, Ni and Mn.