TY - JOUR
T1 - Correction to
T2 - Measures under the flat norm as ordered normed vector space (Positivity, (2018), 22, 1, (105-138), 10.1007/s11117-017-0503-z)
AU - Gwiazda, Piotr
AU - Marciniak-Czochra, Anna
AU - Thieme, Horst
N1 - Publisher Copyright:
© Springer International Publishing AG 2017.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - Mt+(S) is a cone ofM(S) if S is complete, because thenMt+(S) = Ms+(S). In general,Mt+(S) is not a cone ofM(S) because it is not closed. It follows from Remark 4.20 thatMt+(S) is dense inMs+(S). Assume thatMt+(S) is closed and S is separable. Then,Mt+(S) =M+(S). This implies that S is universally measurable; however, not all separable metric spaces are universally measurable ([1, Sect. 11.5]).
AB - Mt+(S) is a cone ofM(S) if S is complete, because thenMt+(S) = Ms+(S). In general,Mt+(S) is not a cone ofM(S) because it is not closed. It follows from Remark 4.20 thatMt+(S) is dense inMs+(S). Assume thatMt+(S) is closed and S is separable. Then,Mt+(S) =M+(S). This implies that S is universally measurable; however, not all separable metric spaces are universally measurable ([1, Sect. 11.5]).
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U2 - 10.1007/s11117-017-0535-4
DO - 10.1007/s11117-017-0535-4
M3 - Comment/debate
AN - SCOPUS:85031751442
SN - 1385-1292
VL - 22
SP - 139
EP - 140
JO - Positivity
JF - Positivity
IS - 1
ER -