A mathematical basis for the digitization of gray value of an image is proposed. This was called Oteru-Koshimizu Quantization Theorem (OK-QT), on the analogy of the Shannon Sampling Theorem (Shannon-ST) for the digitization of the shape of the image. Inspired by the fact that the Shannon-ST is the reconstruction theorem of the analog image from the discrete image, OK-QT was modeled as the reconstruction theorem of the shape of the probability density function of gray values of an image. This is a novel and unique mathematical basis for the digitization of the gray scale of an image. This paper outlines this theorem and also shows some experimental results to demonstrate its practical applicability. Through this, the OK-QT gives a clue to the mathematical paradigm for the complete basis for digitization, together with Shannon ST.