Recently,I am reading kolodziej's acta paper,there are some ditails that i do not know clearly.\\ clearly.

In the top line of page 99,"it's no restriction to assume that for each s we have $\nu(\cup_{I\in{B_s}}\partial I)=0$",i do not know why.Here $\nu=(dd^{c}v)^n$ and $v\in PSH(\Omega)\cap L^{\infty}$,$\partial I$ is the boundary of some cube.\\ cube.

From Kolodziej's view,a poriori $\nu(\cup_{I\in{B_s}}\partial I)$ may not be zero.However,i think $\partial I$ can be seen as a part of a pluripolar set,then according to Bedford and Taylor's reasult,we know the above monge-ampere measure concentrates no mass on $\partial I$.So we get $\nu(\cup_{I\in{B_s}}\partial I)=0$,and it should not be a assumption!\\ Ask for help.thanksassumption!

I hope some expert in this field can help me.Thanks.

recently,i have read

Recently,I am reading kolodziej's acta paper,there are some ditails that i do not know clearly.\newline in clearly.\\ In the top line of page99,"it's page 99,"it's no restriction to assume that for each s we have $\nu(\cup_{I\in{B_s}}\partial I)=0$",i do not know why.\newline ask why.Here $\nu=(dd^{c}v)^n$ and $v\in PSH(\Omega)\cap L^{\infty}$,$\partial I$ is the boundary of some cube.\\ From Kolodziej's view,a poriori $\nu(\cup_{I\in{B_s}}\partial I)$ may not be zero.However,i think $\partial I$ can be seen as a part of a pluripolar set,then according to Bedford and Taylor's reasult,we know the above monge-ampere measure concentrates no mass on $\partial I$.So we get $\nu(\cup_{I\in{B_s}}\partial I)=0$,and it should not be a assumption!\\ Ask for help.thanks.

recently,i have read kolodziej's acta paper,there are some ditails that i do not know clearly.// clearly.\newline in the top line of page99,"it's no restriction to assume that for each s we have...",i have $\nu(\cup_{I\in{B_s}}\partial I)=0$",i do not know why.// why.\newline ask for help.thanks.

recently,i have read kolodziej's acta paper,there are some ditails that i do not know clearly. clearly.// in the top line of page99,"it's no restriction to assume that for each s we have...",i do not know why. why.// ask for help.thanks.

recently,i have read kolodziej's acta paper,there are some ditails that i do not know clearly. in the top line of page99,"it's no restriction to assume that for each s we have...",i do not know why. ask for help.thanks.