I am from engineering background and the concept of Borel set, Borel field and measures sound abstract to me. Can some one please, explain them in a simplified way i.e., to explain them without assuming the reader has any knowledge about measure theory.
For example when I read the function is continuous over some interval, I can visualize it and I know I can integrate it over that interval. But when I read X is the intensity measure for a Borel set, I don't get it and most importantly I don't get what should this imply for the future steps (i.e., if it is a Borel what can I do and if it is not what are the things that I can't do).
Assuming some one will answer these, can you please explain the Lebeg measure in the same manner simplified manner as well.
Hopefully this makes sense.