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barrenness (n.)

late 14c., "incapacity for child-bearing" (of women); "unproductivity, unfruitfulness" (of land); earlier in a figurative sense ("spiritual emptiness," mid-14c.), from barren + -ness.

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Definitions of barrenness from WordNet

barrenness (n.)
the state (usually of a woman) of having no children or being unable to have children;
barrenness (n.)
the quality of yielding nothing of value;
Synonyms: fruitlessness / aridity
From wordnet.princeton.edu