Convert ts to mp4 on fly

Is it possible to convert ts to mp4 on the fly so that the mp4 can be viewed basically as it's being recorded, or at least with a delay. I have been looking into ffmpeg but can't get the grasp on whether it works or not. Even better would be a software that would allow me to capture the ts signal from the Hauppauge 2250. Is this possible?
Thanks for any help