inside the D25 ellipse of the galaxy. An apparent flattening of the XLF is observed at the low luminosities (see Fig. \[cumXLF\]), which may be caused by incompleteness effects. To correct for this, we eliminate the three lower points of the XLF that may be affected by incompleteness (it should be noted that the purpose of this paper is not to study the low-luminosity XLF of NGC4088). As a result, the XLF flattening disappears.

Since the errors in the cumulative XLF are not independent, from now on we use the differential XLF. This allows us to take into account the statistical uncertainties, which are large given the very small number of sources. These errors do not take into account the possibility that $\leq$ 3 sources inside the D25 are AGN.

![Cumulative XLF of NGC4088. The vertical dotted red line shows the cut performed in the XLF to correct for incompleteness.\[cumXLF\]](XLFbg_lum10_37_loglog_withoutfitLINE.pdf)

We fit the differential XLF with a power-law of the form $dN/dL_\mathrm{X}=BL_\mathrm{X}^{-\beta}$ normalized to $10^{37}$ erg s$^{-1}$, where $\beta=\alpha+1$ (Fig. \[diffXLF\]). The Cash statistic (@1979ApJ...228..939C) is used instead of the minimum $\chi^{2}$ method due to insufficient data points for the errors to be described by Gaussian statistics. The fit gives 