Looking for a source: Fourier inversion of $f \in L^1$ Is there a book where I can find a thorough proof of the following assertion?

Let $f \in L^1(\mathbb{R}^d)$ be continuous at zero and $\hat{f}\ge0$. Then $\hat{f} \in L^1(\mathbb{R}^d)$ and
  $$f(t) = \int_{\mathbb{R}^d} \hat{f}(\xi)e^{2\pi i\, t\xi} \,d\xi$$
  almost everywhere.

I'm looking for the context in which this Lemma is stated, more than the actual proof.

I've finally found the source:
E. M. Stein, G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971. $\S$1. Corollary 1.26 (p.15)

In terms of the proof please see here: Proof of Fourier Inverse formula for $L^1$ case
Further to another German reference that rather pays attention to context than proof is here http://www.math.ethz.ch/education/bachelor/seminars/hs2007/harm-analysis/FT2.pdf
