White noise DC component
White noise has no component at any specific frequency since it is a noise density and therefore has energy across a range of frequencies. The range of any given specific frequency, including DC is zero, and therefore the energy at DC (and any specific frequency) is indeed zero. 

In practice you cannot actually observe DC or any specific frequency as a single point as that would require an infinite observation time. However, the longer you observe, the narrower will be the effective range of frequencies you observe and for this reason the mean will be non-zero but approach zero as your observation time approaches infinity.