Proof of Theorem 1, Calulus of Variation, Gelfand and Fomin

Question

This is theorem 1 on page 12 of Gelfand and Fomin. Why $\phi_1[h]-\phi_2[h]= \epsilon_2 ||h||$ instead of $\epsilon_1 ||h||-\epsilon_2||h||$? Is this a typo and he meant some $\epsilon_3=(\epsilon_1-\epsilon_2)$?

Answer 1

Yes, that is a typo. It should have been

$$\varphi_1[h]-\varphi_2[h]=\epsilon_2||h||-\epsilon_1||h||.$$