Kolmogorov's normability criterion

So, let's imagine you have a big room full of toys. How do you know if the toys can fit nicely on a shelf? Well, you could try putting them on the shelf and see if they fit without falling off.

A mathematician named Kolmogorov had a similar idea, but instead of toys and shelves, he was thinking about functions and sets. He was trying to figure out if there is a way to measure how "nice" a set is by looking at its functions.

Kolmogorov said that a set is "normable" if there is a way to measure the distance between any two points in the set using a special kind of function called a "norm." A norm is like a ruler that tells you how far apart two points are.

So, to summarize: Kolmogorov's normability criterion is a way of saying that a set is "nice" if there is a way to measure the distance between any two points in the set using a special kind of function called a "norm."