Let X be a real normed space, A be a non-singleton compact subset of X, m be a probability measure on the Borel -algebra of A such that for each open set V in X with V \ A 6= ?, m(V \A) > 0. For each x, y 2 X, let A(y, x) = {a 2 A: ky −ak < kx−ak}, WA(y, x) = m(A(y, x)),WA(x) = supz2X WA(z, x). We prove that if X is finite-dimensional and x is an interior point of A, thenWA(x) < 1.

Simpson points in normed spaces.

CASINI, EMANUELE GIUSEPPE
1996-01-01

Abstract

Let X be a real normed space, A be a non-singleton compact subset of X, m be a probability measure on the Borel -algebra of A such that for each open set V in X with V \ A 6= ?, m(V \A) > 0. For each x, y 2 X, let A(y, x) = {a 2 A: ky −ak < kx−ak}, WA(y, x) = m(A(y, x)),WA(x) = supz2X WA(z, x). We prove that if X is finite-dimensional and x is an interior point of A, thenWA(x) < 1.
1996
Baronti, M.; Casini, EMANUELE GIUSEPPE
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1792846
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