I am reading Bartle's "The Elements of Integration" and am at the part where he proves Lemma 2.11: If $f$ is a nonnegative function in $M(X,X)$, then there exists a sequence $(\phi_n )$ in $M(X,X)$ such that:
(a) $0 \leq \phi_n (x) \leq \phi_{n+1} (x)$ for $x\in X, n\in\mathbb{N}$ and some other conditions (b), (c).
However later $\phi_n$ is defined to be $k 2^{-n}$, which seems to contradict property (a) above.
Is there something I missed? Thanks!