Locally integrable function

A locally integrable function is a type of function that can be split into small pieces and then added up to give the whole function.

Think of it like a puzzle - you have a big picture made up of lots of small puzzle pieces. Each piece on its own might not make much sense, but when they are all put together, you have a complete picture.

A locally integrable function is like that; you have a big picture (the function) made up of lots of small pieces (or intervals). When you add up all of these small pieces (or integrate them), you get the whole function.

But it's important to note that not all functions can be split up this way. Some functions might have tiny, weird-shaped pieces that can't be added up properly. Those functions are not locally integrable.

So, in summary, a locally integrable function is a function that can be broken down into small pieces and then added up to give the whole function.