district vs inner city

district

noun
  • An area or region marked by some distinguishing feature. 

  • the Soho district of London 

  • An administrative division of an area. 

  • An administrative division of a county without the status of a borough. 

verb
  • To divide into administrative or other districts. 

inner city

noun
  • The interior, central part of a city, as opposed to the suburbs 

How often have the words district and inner city occurred in a corpus of books? (source: Google Ngram Viewer )