Final answer:
While the term 'Big Three' generally refers to the leaders of the Allied nations during WWII, in terms of record companies of the late 1930s, RCA Victor, Columbia Records, and Decca Records were the dominant players in the music industry.
Step-by-step explanation:
The question pertains to the late 1930s and asks about the most important record companies during that time. However, there seems to be a confusion with the term 'Big Three' as it was coined to describe the leaders of the three major Allied nations during World War II - Winston Churchill, Franklin Roosevelt, and Joseph Stalin - which does not relate directly to record companies.
In regard to the music industry of the late 1930s, the three most notable American record companies that were often referred to as the 'big three' were RCA Victor, Columbia Records, and Decca Records. These companies were instrumental in the music industry, signing major artists and influencing music trends of the era.
As the question does not align precisely with historical accounts, one can infer that it aimed at understanding which record companies dominated the music industry prior to World War II.
The complete question is: In the late 1930s, which were the three most important record companies? is: