By using the same techniques as Proposition 2.2, we get mathbb{E} sup_{0 leqthetaleq tau} bigl(bigl|(CV) (theta) - (C G_{l}) (theta bigr|^{2}bigr) leq (2tau+ 8) mathbb{E} int_{0}^{tau} h(theta) gbigl(bigl|Vbigl(f(theta) bigr) - G_{l}bigl(f(theta )bigr bigr|^{2}bigr),dtheta.
where and Moreover, by using the same argument as in Proposition 3.5, we have for every and Thus, (3.35).
Now we prove that this is enough for getting an extension of T 0 that coincides with T using the same construction that proves Proposition 2.7 in [31].
If the function ψ ̃ is concave it is not difficult to prove using the same idea as in Proposition 7, that, for λ > 1, it yields that ψ ̃ ( s, t ) s ≥ ψ ̃ ( λ s, λ t ) λ s and ψ ̃ ( s, t ) 1 - s ≥ ψ ̃ ( λ s, λ t ) 1 - λ s.
Next, using the same reasoning as in Proposition 1, it is easy to check that when (z^{prime }(F le 0), CC leads not only to a fall of (e_{T}) and R when F goes up but also to a fall in (tau ).
Using the same method in the proof of Proposition 2.1, we see that (delta=0), which completes the proof.
By using the same argument as in the proof of Proposition 3.1(c), we obtain that.
Using the same computations than in the proof of Proposition 3.1 and using the bound (33) on R, we obtain Theorem 2.3.
By using the same arguments presented in the proof of Theorem 2, the desired result follows directly from Proposition 3. □.
When Russell argues that 'author of Waverly' cannot mean the same as 'Scott' because this would imply that 'Scott is the author of Waverley' and 'Scott is Scott' express the same proposition, he uses 'meaning' in an intensional sense: "plainly intension (or connotation) of the author of Waverley and of Scott, cannot be the same".
