How to implement "greater than" based on dimension value in MDX

You can use your below expression when the dimension members are numericly arranged

WHERE ([Dim Company Info].[Gdp Growth].&3 : [Dim Company Info].[Gdp Growth].&3.LastChild) with a slight correction

WHERE ([Dim Company Info].[Gdp Growth].&[3] : [Dim Company Info].[Gdp Growth].[Gdp Growth].LastChild)

However if that is not the case, then you need to follow the below method.

I am reporting the product with the max quantity.

select {[Measures].[Internet Sales Amount]} on 0,
non empty
([Product].[Product].[Product],[Promotion].[Max Quantity].[Max Quantity]) on 1 
from [Adventure Works]

Now lets manipulate the max quantity to make it behave like a measure.

with 
member measures.test
as 
case when [Measures].[Internet Sales Amount]>0 then 
(nonempty(([Product].[Product].currentmember,[Promotion].[Max Quantity].[Max Quantity]),[Measures].[Internet Sales Amount])).item(0).item(1).name
else 
null end

select
{[Measures].[Internet Sales Amount],measures.test}
on 0,
non empty ([Product].[Product].[Product] )
on 1 
from [Adventure Works]

Now you can use the filter, but we need to cast(note the use of CInt) the data too

with 
member measures.test
as 
case when [Measures].[Internet Sales Amount]>0 then 
Cint((nonempty(([Product].[Product].currentmember,[Promotion].[Max Quantity].[Max Quantity]),[Measures].[Internet Sales Amount])).item(0).item(1).name)
else 
null end

select
{[Measures].[Internet Sales Amount],measures.test}
on 0,
non empty (
filter(
[Product].[Product].[Product]
,measures.test>0) 
)
on 1 
from [Adventure Works]