Is it better to say:
The amount of deals in the Ukrainian venture capital market reached $832 million
OR
The volume of deals in the Ukrainian venture capital market reached $832 million

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I would say value instead, but the better option here would be volume... Amount sounds like you are talking about the number of deals rather than the value of them.

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I agree with Camilla. It does look like we're talking about the value of the deals here. :)

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I think I would use value (or dollar value) rather than amount or volume.

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Volume.