= Solution
In the <microcanonical ensemble>, the <microcanonical energy-shell entropy> is the <Boltzmann entropy>
$$
\boxed{S(E,V,N;\delta E)=k_B\log\Omega(E,V,N;\delta E).}
$$
For a macroscopic system, changing the small energy resolution by a fixed factor changes $\log\Omega$ only by a nonextensive additive term, while $S=O(Nk_B)$. Its relative effect therefore vanishes in the <thermodynamic limit>.
The <thermodynamic temperature>, <pressure>, and <chemical potential> are defined in the entropy representation by
$$
\frac1T=\left(\frac{\partial S}{\partial E}\right)_{V,N},
\qquad
\frac PT=\left(\frac{\partial S}{\partial V}\right)_{E,N},
\qquad
-\frac\mu T=\left(\frac{\partial S}{\partial N}\right)_{E,V}.
$$
Thus
$$
dS=\frac1T dE+\frac PT dV-\frac\mu T dN,
$$
or, equivalently, the <first law of thermodynamics> in fundamental form is
$$
\boxed{dE=T dS-P dV+\mu dN.}
$$
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