Green’s Dictionary of Slang

(US black/jazz) the Storyville area of New Orleans, centre of the city’s jazz community.

1948		Malone & Vandervoort Trumpet on the Wing 11: I never played in ‘the district’.
1955		Shapiro & Hentoff Hear Me Talking to Ya 4: I never heard it called Storyville [...] It was always The District — the red light district.