Measures of weak non-compactness in l1()-spaces

Disjoint sequence methods from the theory of Riesz spaces areused to study measures of weak non-compactness inL1(mu)-spaces. A principalnew result of the present paper is the following: LetEbe an abstractM-space.Then omega(B)=sup{lim supn ->infinity rho B(xn):(xn)n subset of BEdisjoint} =inf{epsilon>0:there exists x & lowast;is an element of E & lowast;+so thatB subset of[-x & lowast;,x & lowast;]+epsilon BE & lowast; =sup{lim supn ->infinity rho B(xn):(xn)n subset of BEweakly null =sup{ca rho B((xn)n):(xn)n subset of(BE)+increasing=sup{lim supn ->infinity & Vert;x & lowast;n & Vert;:(x & lowast;n)n subset of Sol(B) disjoint=sup{lim supn ->infinity supx & lowast;is an element of B|< x & lowast;,xn >|:(xn)n subset of BEdisjoint} for every norm bounded subsetBofE & lowast;.