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Luminosity density means "luminosity per unit volume", and is a measure used in large scales, such as "the luminosity density of the local universe", or smaller e.g., the luminosity density of a particular portion of the Milky Way.
The phrase luminosity density can also arise in discussions of the counts of galaxies or stars with different luminosities, e.g., discussions of luminosity functions, in which case density refers to a probability density.