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Product over an arbitrary index.

I have a function f(x,y)   that I would like to compute the product
over indices i,j
where i goes from an arbitrary list {1,4,3}  and j goes 1 to m.

Is this possible in mathematica the function Product itself seems to
only work over a continous sequence and it is not clear how I can use
two set of indices.

Additionally can I specify the product over an intersection or
complement of a list?.

K Frou

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