A problem in understanding distributions exercise

[Goldbeetle]

I'm reading the first chapters of "A Guide to Distribution Theory and Fourier Transforms".
On page 10, Exercises 3,6,7 the distribution is defined in terms of integrals. The first one is always without integrand (there's only the integral sign). What does that mean? Am I missing something? The book can be consulted online in Google Books.

Thanks for any help!

Goldbeetle

 

[BruceG]

I think it is just you intergrate over two disconnected ranges (-inf,-a) + (+a,+inf).

 

[arkajad]

Exactly

$$\int_{-\infty}^{-a}+\int_{a}^{\infty}\;f(x)dx=\int_{-\infty}^{-a}\;f(x)\;dx+\int_{a}^{\infty}\;f(x)\;dx$$

 

[Goldbeetle]

OK, thanks.