Welcome aboard.
The marble is Greek, I think, and many white Greek "marbles" are mostly crystal, which fractures easily.
Marble in general is about the softest stone known to people like us, and as Bud said, it takes a lot of underpinning to make a sucessful installation.
What we would need to know:
What size are the joists or trusses that support the subfloor?
How far apart are they?
What does the subfloor consist of, i.e., plywood (how thick, how many layers?).
Was the concrete backer board bedded in thin set mortar and then fastened?
What is the overall span of the joists or trusses from support to support?
Are the joists or trussed "bridged" at mid-span or anywhere in the span?
If we know all of the above, we will be able to take a GUESS at the amount of deflection you are likely to accrue.
If it's over 1/720th of the span, we'll recommend going to an alternate flooring.
Please give us a short name to call you by. It can be an alias.