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1.
A man's sleeveless undershirt. White, or at least once-white.

Also called IDJ or an Italian tuxedo.
Bruno wore his Italian dinner jacket to Angelo and Carla's wedding.
by Cap'n Bullmoose April 23, 2005
 
2.
A sleevless T shirt also known as a wife beater or guinea tee.
Uncle tony's all dressed up in his Italian dinner jacket for sunday gravy.
by garand March 06, 2011