Kahler spaces are just certain singular spaces equipped with a Kahler metric in appropriate sense. I first came across it Demaily-Paun's classical paper [Numercical Characterization of the Kahler cone of a compact Kahler manifold](https://annals.math.princeton.edu/wp-content/uploads/annals-v159-n3-p05.pdf). However it seems to refer the reader to the relevant background material in another paper of Demaily which is in French. I wonder whether there is any reference that have some background materials on Kahler spaces: definition, fundamental properties etc.



reference request for singular Kahler space
There is a discussion of this topic in the recent book [Cycles analytiques complexes II : l'espace des cycles](https://smf.emath.fr/publications/cycles-analytiques-complexes-ii-lespace-des-cycles) by Barlet and Magnússon, chapter XII.3. An English translation (to be published by Springer) is forthcoming.


You will also find a short discussion in the book [Degenerate Complex Monge–Ampère Equations](https://www.ems-ph.org/books/book.php?proj_nr=210) by Guedj and Zeriahi, chapter 16.3.


