On the defninition of white noise, a question concerning the notes on SPDE's from Walsh

Question

In page 5 from the notes "An introduction to SPDE's" from Walsh, one reads:

According to this definition $W(\emptyset) $ is not $0$. Isn't this a typo on the notes, I mean, shouldn't it be

$$W(A \cup B) = W(A) + W(B)?$$