Trainin came to prominence in the inter-war years as critical of the League of Nations for not doing enough to prosecute the those who waged war against peace. Scholars of the University of Wisconsin–Madison, of the National University of Singapore, and Michelle Jean Penn of the University of Colorado Boulder credit him with establishing the international legal concept of "crimes against peace". In 1937 Trainin published his 'The Defense of Peace and Criminal Law' in which he castigated the League of Nations for failing to make aggressive war a criminal offense and not providing for any sort of international court to punish aggressors. Along with Major-General Iona Timofeevich Nikitchenko, who also served as a judge, Trainin was a signatory for the Soviet Union to the charter of the Allies of World War II War Crimes Executive Committee which established the Nüremberg International Military Tribunal for "the prosecution and punishment of the major war criminals of the European Axis", known in Russian as the "London Agreement", ".