The perinuclear space of the nuclear envelope is continuous with:
Nuclear envelope architecture features inner membrane containing lamina-binding proteins emerin and lamin B receptor, outer membrane studded with ribosomes and functionally similar to rough ER, and intervening perinuclear space twenty to fifty nanometers wide that is direct extension of ER lumen. This topology allows shared environment for oxidative protein folding, calcium storage and lipid synthesis enzymes in outer membrane, and rapid diffusion of luminal chaperones BiP, calreticulin and protein disulfide isomerase between compartments. No such continuity exists with Golgi lumen because Gol
Ref: Alberts Ch 12; perinuclear space continuous with ER lumen, not Golgi lysosome mitochondrial matrices.