Abstract: This paper  designed to study the core equivalence problem ininfinite dinensional commodity spaces by using  nonstandad analysis.Let  X be  a  superstructure,k>card(X) a  regular  cardinal,and·Xa K-saturated ncnstandard extengion of  A nonstandsrd exchange economy inodel is established on a commodity space F,where  a standard normed Riesz space.in this model the set of consumers is a   hyperfinite(reaily    infinite)set, dencted   by    T=(1,2,…,o}(m∈·N-N),and   the   preference    of each consumer t is an internal bindiy relation >on his consumption set Xisuch that xpu for any x∈X. Each consumption      se:”assuned  satisfy      that(1).intEx,AB≠Ø,and(2).y<z      implies      y∈ X,for  any  x∈nsX:and  y∈ns"R.It  s  showed  that  if the  preferences  are  monotonic  for  almost  ll consumers,then the core of the economy coincides with the set of all competitive equilibria.It is also showed that when the set of comsumers who have monotonic preferences is nonnegligible,an allocation is an core allocation if and only if it is supported by prices,and if and only if it is strongly supported by prices.

Key words: preference, monotone, S-topology, K-measure, allocation, corejsupporting price, competitive equation