This is from Jurgen Weibull's textbook on game theory, page 10, where an example is introduced.
The author claims that the player's third strategy is not weakly dominated by other two pure strategies.
This is obviously false. The third strategy gives a payoff of 1. Whereas the first strategy gives a payoff of 3. $$3 > 1.$$
This means that the third strategy is strictly dominated by the first one and strict dominance implies weak dominance.
Is this an error in the textbook or did I misinterpret something?
$A$ dominates $B$ if I prefer to play $A$ over $B$ regardless of the actions of my opponent. This is not true here, as if the column player plays R, I would rather play the third action over the first, so the first does not dominate the third. The same goes with the second and the third.
As the textbook says, there is mixed dominance here: I prefer to mix the first two actions with equal probabilities over (payoff 1.5) over playing the third one (payoff 1).