Let $$\mathfrak {X}^{0,1}_\nu (M)$$
X
ν
0
,
1
(
M
)
be the subset of divergence-free Lipschitz vector fields defined on a closed Riemannian manifold M endowed with the Lipschitz topology $$\Vert \,{\cdot }\,\Vert _{0,1}$$
‖
·
‖
0
,
1
where $$\nu $$
ν
is the volume measure. Let $$\mathfrak {X}^{0,1}_{\nu ,\ell }(M)\subset \mathfrak {X}^{0,1}_\nu (M)$$
X
ν
,
ℓ
0
,
1
(
M
)
⊂
X
ν
0
,
1
(
M
)
be the subset of vector fields satisfying the $$\ell $$
ℓ
-property, a property that implies $$C^1$$
C
1
-regularity $$\nu $$
ν
-almost everywhere. We prove that there exists a residual subset "Equation missing" with respect to $$\Vert \,{\cdot }\,\Vert _{0,1}$$
‖
·
‖
0
,
1
such that Pesin’s entropy formula holds, i.e. for any "Equation missing" the metric entropy equals the integral, with respect to $$\nu $$
ν
, of the sum of the positive Lyapunov exponents.