  The concept of sample mean in dynamic time warping (DTW) spaces has been
successfully applied to improve pattern recognition systems and generalize
centroid-based clustering algorithms. Its existence has neither been proved nor
challenged. This article presents sufficient conditions for existence of a
sample mean in DTW spaces. The proposed result justifies prior work on
approximate mean algorithms, sets the stage for constructing exact mean
algorithms, and is a first step towards a statistical theory of DTW spaces.
