A set \(E\) in the unit disc \(\mathbb{D}\) is a set of determination for a family of functions analytic in \(\mathbb{D}\) if \(\sup_E|f|= \sup_{\mathbb{D}}|f|\) for all \(f\) in the class. The Nevanlinna class \({\mathcal N}\) comprises all functions \(f\) analytic in \(\mathbb{D}\) with \[ \sup_{0<r<1} \int^{2\pi}_0\log^+|f(re^{i\theta})|\,d\theta< \infty. \]
For \(n\in\mathbb{N}\) and \(m\in\mathbb{Z}\) with \(0\leq m< 2^{n+4}\), let
\[ z_{m,n}= \left(1-2^{-n}\right)\exp\left(2\pi im/2^{n+4}\right), \]
\[ S_{m,n}= \Big\{re^{i\theta}: 2^{-n-1}\leq 1- r\leq 2^{-n},\;2\pi m/2^{n+4}\leq \theta\leq 2\pi(m+1)/2^{n+ 4}\Big\} \]
and \(E_{m,n}= E\cap S_{m,n}\); and let \(P\) be the Poisson kernel \(P(z,w)= (1-|z|^2)/|z- w|^2\) for \(\mathbb{D}\) (\(z\in\mathbb{D}\), \(w\in\mathbb{T}= \{|x|= 1\}\). Also, for any set \(A\) contained in a disc of radius less than 1, and any \(t\geq 0\), let \(Q(A, t)= 0\) if \(t= 0\) or \(A=\emptyset\); otherwise let \[ Q(A,t)= \min\Biggl\{k\in \mathbb{N}: \exists\xi_1,\dots, \xi_k\in\mathbb{C}\text{ such that }\sum^k_{j=1}\log 1/|z-\xi_j|\geq t\;(t\in A)\Biggr\}. \] The author proves that a set \(E\subset\mathbb{D}\) is a set of determination for \({\mathcal N}\) if and only if \[ \sum_{m,n} 2^{-n}Q\big(2^n E_{m,n},[P(z_{m,n}, w)]\big)= \infty \] for every \(w\in\mathbb{T}\), where \([\,\cdot\,]\) is the integer part function. This extends similar results for sets of determination in the Smirnov class \({\mathcal N}^+\) due to X. Massaneda and P. J. Thomas [Rev. Mat. Iberoam. 24, No. 1, 353–385 (2008; Zbl 1160.30020)] and for the Hardy space \(h^1\) due to W. K. Hayman and T. J. Lyons [J. Lond. Math. Soc., II. Ser. 42, No. 2, 292–308 (1990; Zbl 0675.30040)].