I have a property that i claimed rent for last year on schedule e. In 2016 I didnt rent out this property. I have 0 rent but can I still claim expenses such as depreciation expense?

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 The key in this  is that the property was available for rent and the owner was looking for a tenant, even though he or she hadn't found one yet. 

The lack of evidence of a rental property business strategy,and the fact you have no cash flow generate from the property.You should be trying to generate revenue and if what you try does not work, you should try something else.  And be able to document it.

Generally advertising expenses is a factor in the business strategy to  maintain as an active rental