On a Characterisation of Inner Product Spaces
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Abstract It is well known that for the Hilbert space H the minimum value of the functional F μ (f) = ∫ H ‖f – g‖2 dμ(g), f ∈ H, is achived at the mean of μ for any probability measure μ with strong second moment on H. We show that the validity of this property for measures on a normed space having support at three points with norm 1 and arbitrarily fixed positive weights implies the existence of an inner product that generates the norm.
2018 ◽
pp. 339
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2006 ◽
Vol 4
(1)
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pp. 1-6
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1996 ◽
Vol 15
(4)
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pp. 515-518
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