The X-ray galaxy cluster sample from the REFLEX Cluster Survey, which covers the X-ray brightest galaxy clusters detected in the ROSAT All-Sky Survey in the southern sky, is used to construct the X-ray luminosity function of clusters in the local Universe. With 452 clusters detected above an X-ray flux-limit of 3 10^(-12) erg s^(-1) cm^(-2) in 4.24 sr of the sky, this sample is the most comprehensive X-ray cluster sample with a well documented selection function, providing the best current census of the local X-ray galaxy cluster population. In this paper we discuss the construction of the luminosity function, the effects of flux measurement errors and of variations with sample region and we compare the results to those from previous surveys.
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