I just started reading this paper
[Periodic Unfolding method][1] [1]: https://www.researchgate.net/publication/220132127_The_Periodic_Unfolding_Method_in_Homogenization
where in the definition 1.2: for each $x \in R^{N}$, one has $x = \epsilon( [\frac{x}{\epsilon}]_{Y} + \{\frac{x}{\epsilon}\}_{Y})$ where $[.]$ gives the integer or position of a point in $\Omega$ the open set and $\{.\}$ stands for position in reference cell.\
$Ξε =\{ξ ∈ Z^{N},ε(ξ +Y )⊂Ω\}$, \ $ Ωε = interior\{ \cup_{ξ∈Ξε} \, ε(ξ +Y)\}$,\ $Λε = Ω - Ωε$.\
The set $Ωε$ is the largest union of $ε(ξ + Y)$ cells $(ξ ∈ Z^{n})$ included in $Ω$, while $Λε$ is the subset of Ω containing the parts from ε(ξ+Y)cells intersecting the boundary ∂Ω.
Then in the proof of preposition 2.5 I am missing the point how? $|εξ +εY|\int_{Y} φ(εξ +εy)dy = ε^{n}|Y| \int_{Y} φ(εξ +εy) dy $.
If someone just skip his or her 2 minutes please. Thanks in advance