The John-Nirenberg type inequality for non-doubling measures
X. Tolsa defined a space of BMO type for positive Radon measures satisfy- ing some growth condition on R d . This new BMO space is very suitable for the Calderon- Zygmund theory with non-doubling measures. Especially, the John-Nirenberg type in- equality can be recovered. In the present paper we introduce a localized and weighted version of this inequality and, as applications, we obtain some vector-valued inequalities and weighted inequalities for Morrey spaces.