Its statement is as follows.
- Let B ⊂ E be a bounded, closed, convex set of a real Banach space E. Then the set
- is norm-dense in the dual . Note, this theorem fails for complex Banach spaces 
- Bishop, Errett; Phelps, R. R. (1961). "A proof that every Banach space is subreflexive". Bulletin of the American Mathematical Society. 67: 97–98. doi:10.1090/s0002-9904-1961-10514-4. MR 0123174.
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