the following is from Understanding Machine Learning: Theory to Algorithm textbook:

Definition of PAC Learnability: A hypothesis class $H$ is PAC learnable if there exist a function $m_H : (0, 1)^2 \rightarrow \mathbb{N}$ and a learning algorithm with the following property: For every $\epsilon, \delta \in (0, 1)$, for every distribution $D$ over $X$, and for every labeling function $f : X \rightarrow \{0,1\}$, if the realizable assumption holds with respect to $H,D,f$ then when running the learning algorithm on $m \ge m_H(\epsilon,\delta)$ i.i.d. examples generated by $D$ and labeled by $f$, the algorithm returns a hypothesis $h$ such that, with probability of at least $1 - \delta$ (over the choice of the examples), $L_{(D,f)}(h) \le \epsilon$.

1. In the function definition $m_H : (0, 1)^2 \rightarrow \mathbb{N}$; what does a) 0 and 1 in the bracket, b) the integer 2, and c) $\rightarrow \mathbb{N}$ refer to?

Thank you!

The following is from Understanding Machine Learning: Theory to Algorithm textbook:

Definition of PAC Learnability: A hypothesis class $\mathcal H$ is PAC learnable if there exist a function $m_H : (0, 1)^2 \rightarrow \mathbb{N}$ and a learning algorithm with the following property: For every $\epsilon, \delta \in (0, 1)$, for every distribution $D$ over $X$, and for every labeling function $f : X \rightarrow \{0,1\}$, if the realizable assumption holds with respect to $\mathcal H,D,f$ then when running the learning algorithm on $m \ge m_H(\epsilon,\delta)$ i.i.d. examples generated by $D$ and labeled by $f$, the algorithm returns a hypothesis $h$ such that, with probability of at least $1 - \delta$ (over the choice of the examples), $L_{(D,f)}(h) \le \epsilon$.

1. In the function definition $m_H : (0, 1)^2 \rightarrow \mathbb{N}$; what does a) 0 and 1 in the bracket, b) the integer 2, and c) $\rightarrow \mathbb{N}$ refer to?