Yes, you can use marble, so long as it is sealed. The concern here is that because marbles (and limestone and travertine) contain calcium carbonate, the polished surface is more vulnerable to household acids including vinegar, mustard, citrus and a host of other food-related products. 

Additionally, marble and limestone can be scratched more easily than harder stones such as granite. 

However marble is still a very strong surface when compared to other materials. This said, marble is still an excellent hygienic surface for kitchens. The choice is a balance between aesthetics and practicality. If you seal and take care of your marble kitchen, then there is less of a chance of damage. The other choice is a engineered stone, giving choice of marble looking stone, with a very durable surface.