Bochner space

Bochner spaces are mathematical spaces that are measured by a certain kind of "measuring stick". In a Bochner space, it's like the measuring stick is made up of curves, not like a regular ruler. For example, if you wanted to measure two points on a Bochner space, you would draw a curve from one point to the other and measure the length of the curve. These special measuring sticks are called metrics and they help to calculate distances between objects in a Bochner space.