In this chapter, we extend the semantic information measures, such as semantic entropy, semantic mutual information to the continuous message. Firstly, we give the definitions of semantic entropy and mutual information in the continuous case. Secondly, we investigate the capacity of Gaussian channel in the semantic sense and obtain the semantic channel capacity formula of band-limited Gaussian channel, which is an important extension of the famous Shannon channel capacity formula. Finally, we derive the semantic rate-distortion function for the Gaussian source.