What does orthogonality mean for basis functions in Fourier transform?

Hi! In Fourier transform, the basis functions are $\displaystyle e^{j\omega t}$, where $\displaystyle \omega$ is unique for each basis function. But what does it mean that two basis functions are orthogonal? The ordinary integral for the inner product

$\displaystyle \int\limits_{-\infty}^{+\infty}f^*(t)g(t)dt$

cannot be used here to indicate orthogonality, because the integral would not converge. So what does orthogonality in this case really mean? I have looked in a few articles at Wikipedia, but it is not mentioned anywhere that this integral will actually not converge (at least not in the normal sense) for two functions of this kind. In the Fourer transform article, orthogonality between two different basis functions is not even mentioned.