What is the definition of "square integrable function"?

Question

Does it make a difference to say it is "square integrable on [0, 1]^d", where [0, 1]^d represents the d-dimensional unit cube?

Answer 1

A square integrable function is that which the definite integration of its square (absolute value of its square for complex functions) from -∞ to +∞ is less than infinity. It's an important requirement for integral transforms, such as fourier transforms. But I imagine that to say a function is "square integrable on [0,1]^d" means that the integration is carried from those limits of the hypercube, and that the result is less than infinity.

Answer 2

Square Integrable

Answer 3

I think the definition of a "great wrestler" is bias. Because you know that everyone who is going to answer is going to pick out their favorite wrestler. The fact that a wrestler must be able to give out great moves is a necessity and I'm not going to lie...Shawn Michaels is an amazing wrestler, I think his moves reflects his character but that can work out to his advantage because he's a little guy compared to the others. Plus the fact that he has the ability to entertain a crowd through his moves speaks for itself. Anyone of this list is a great wrestler but they are limited to what they are told to do or what their character is portrayed. However, you get guys like Batista or Hogan and from a wrestling standpoint they have NONE. Hogan makes up for his lack of moves by selling promos but Batista has none, he doesn't have mic skills nor does he have technical skills. You can tell because he has been in this company for a long time and he has yet to update any of his moves. The moves are scripted but wrestlers are only told of how long they are going to perform or who is going to win. Batista would've had the freedom to execute any wrestling move but instead we get clothesline after clothesline and then some hits here and there and then a Batista bomb.

Answer 4

(M)

In mathematics, an integrable function is a function whose integral exists. Unless specifically stated, the integral in question is usually the Lebesgue integral. Otherwise, one can say that the function is "Riemann-integrable" (i.e., its Riemann integral exists), "Henstock-Kurzweil-integrable," etc. Below we will only examine the concept of Lebesgue integrability.