2 ms·
If you want, but you can do better. I believe, for instance, that at least continuous functions on the reals have a countable basis. Might even be as strong as
by ravi-delia 4y ago
If you want, but you can do better. I believe, for instance, that at least continuous functions on the reals have a countable basis. Might even be as strong as measurable, not sure about that. That's how, for instance, fourier transforms work.
- constantcrying 4y agoThe fourier Transform essentially means that every L^2 (the square of the function has a finite integral) is completely "described" by an l^2 series (a series of numbers whose sum of squares converges), which is about the greatest piece of magic in mathematics. One very important piece here is that the term "function" is somewhat of a lie (since the result couldn't be true if it weren't). The result for measurable functions (not almost functions) shouldn't be true (I think). I am not even sure it is true for L^1 almost functions.