In this paper, the probabilistic relations of dual morphological operations, such as dilation and erosion, closing and opening, and close- open and open-close, and the statistical properties for a continuous stationary lst order Gauss-Markov source are analyzed. The result is that the dual filters have symmetrical means and skews, and equal variances. Also, the statistics of morphological filters are very similar with those of input source, as correlation coefficient increases.