1) uniform rotundity points in measure
依测度一致凸点
1.
A new definition,namely uniformly rotundity points in measure,is introduced,and the criteria for the uniform rotundity points in measure of Orlicz spaces with the Orlicz norm are given.
引进依测度一致凸点的概念,给出了赋Orlicz范数Orlicz空间依测度一致凸点的判据,进而推出Orlicz空间依测度一致凸的充分必要条件。
2) uniform rotundity in measure
依测度一致凸
1.
The necessary and sufficient conditions of the uniform rotundity in measure of Orlicz spaces are obtained too.
引进依测度一致凸点的概念,给出了赋Orlicz范数Orlicz空间依测度一致凸点的判据,进而推出Orlicz空间依测度一致凸的充分必要条件。
3) UR point
一致凸点
4) WUR point
弱一致凸点
5) midpoint locally uniformly convex
中点局部一致凸
1.
It is shown that Banach space X is locally uniformly non square if and only if d X(x,1)>0 for all x∈S(X) ; X is strongly strictly convex if and only if whenver for any x∈S(X),y n∈S(X) and α∈R, if ‖x+αy n‖→0 , and ‖x-αy n‖→1, then α=0 ;and X is strongly strictly convex if and only if X is midpoint locally uniformly convex.
证明了Ｂａｎａｃｈ空间Ｘ是局部一致非方的当且仅当对任意ｘ∈Ｓ（Ｘ），都有ｄＸ（ｘ，１）＞０；Ｘ是强严格凸的当且仅当对任意ｘ∈Ｓ（Ｘ），ｙｎ∈Ｓ（Ｘ）和α∈Ｒ，若‖ｘ＋αｙｎ‖→１和‖ｘ－αｙｎ‖→１，则α＝０；并证明了Ｘ是强严格凸的充要条件为Ｘ是中点局部一致凸
6) local uniform convex point
局部一致凸点
1.
Lastly, it presents a necessary condition for local uniform convex point.
最后给出了局部一致凸点的一个必要条件。
补充资料：依测度收敛
依测度收敛
convergence in measure
依侧度收徽【。刃犯吧en理in meas城;。朋口.M0cT‘n。Me衅』 见收徽性的类型(conve卿n优，tyPesof).
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条