caa a22 4500 38638598X CHVBK 20180307112058.0 cr unu---uuuuu 161130e198901 xx s 000 0 eng 10.1017/S0305004100001468 doi S0305004100001468 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100001468 Sun Yeneng Department of Mathematics, University of Illinois, Urbana, Illinois 61801, U.S.A. A nonstandard proof of the Riesz representation theorem for weakly compact operators on C(Ω) [Elektronische Daten] [Yeneng Sun] An easy way to construct the representing vector measures of weakly compact operators on C(Ω) is given by using the Loeb measure technique. This construction is not based on the Riesz representation theorem for linear functionals; thus we have a uniform way to treat the scalar and vector cases. Also the star finite representations of regular vector measures follow from the proof. Copyright © Cambridge Philosophical Society 1989 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 141-145 0305-0041 105:1<141 1989 105 PSP https://doi.org/10.1017/S0305004100001468 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100001468 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sun Yeneng Department of Mathematics, University of Illinois, Urbana, Illinois 61801, U.S.A NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 141-145 0305-0041 105:1<141 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge