As used in this chapter, the term “district” means the district within which lie the lands deemed by the legislative body to be benefited by the establishment of the pedestrian mall, the boundaries of which have been finally fixed and established pursuant to Section 11500, and in this event such district so established shall be the “district” within the meaning of this chapter even though the legislative body may have determined pursuant to Section 11505 that assessments shall not be levied as contemplated by Section 11202.