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See section 5 (called "Generating generic sequences by iterating j") of Radin's paper Adding closed cofinal sequences to large cardinals.

More details: The iteration is the usual one, using $j$. Now the point is that is $u$ is the measure sequence in $V$, then there is $\sigma: ORD \to V$ so that $\sigma(\alpha)=j_{0, \alpha}(u)\restriction \beta_\alpha,$ for some suitable $\beta_\alpha$ and such that for any $\alpha, \sigma \restriction \alpha+1$ is $\mathbb{R}_{\sigma(\alpha)}$-generic over $M_\alpha$.

See section 5 (called "Generating generic sequences by iterating j") of Radin's paper Adding closed cofinal sequences to large cardinals.

More details: The iteration is the usual one, using $j$ (see my comment below). Now the point is that is $u$ is the measure sequence in $V$, then there is $\sigma: ORD \to V$ so that $\sigma(\alpha)=j_{0, \alpha}(u)\restriction \beta_\alpha,$ for some suitable $\beta_\alpha$ and such that for any $\alpha, \sigma \restriction \alpha+1$ is $\mathbb{R}_{\sigma(\alpha)}$-generic over $M_\alpha$.

See section 5 (called "Generating generic sequences by iterating j") of Radin's paper Adding closed cofinal sequences to large cardinals.

More details: The iteration is the usual one, that is described in the comment below. Now the point is that is $u$ is the measure sequence in $V$, then there is $\sigma: ORD \to V$ so that $\sigma(\alpha)=j_{0, \alpha}(u)\restriction \beta_\alpha,$ for some suitable $\beta_\alpha$ and such that for any $\alpha, \sigma \restriction \alpha+1$ is $\mathbb{R}_{\sigma(\alpha)}$-generic over $M_\alpha$.

See section 5 (called "Generating generic sequences by iterating j") of Radin's paper Adding closed cofinal sequences to large cardinals.

More details: The iteration is the usual one, using $j$. Now the point is that is $u$ is the measure sequence in $V$, then there is $\sigma: ORD \to V$ so that $\sigma(\alpha)=j_{0, \alpha}(u)\restriction \beta_\alpha,$ for some suitable $\beta_\alpha$ and such that for any $\alpha, \sigma \restriction \alpha+1$ is $\mathbb{R}_{\sigma(\alpha)}$-generic over $M_\alpha$.

See section 5 (called "Generating generic sequences by iterating j") of Radin's paper Adding closed cofinal sequences to large cardinals.

More details: The iteration is the usual one, the first step using the normal measure created by $j$. The more strength of $j$ is used to create the measure sequence of enough length in $V$. Now the point is that is $u$ is the measure sequence in $V$, then there is $\sigma: ORD \to V$ so that $\sigma(\alpha)=j_{0, \alpha}(u)\restriction \beta_\alpha,$ for some suitable $\beta_\alpha$ and such that for any $\alpha, \sigma \restriction \alpha+1$ is $\mathbb{R}_{\sigma(\alpha)}$-generic over $M_\alpha$.

See section 5 (called "Generating generic sequences by iterating j") of Radin's paper Adding closed cofinal sequences to large cardinals.

More details: The iteration is the usual one, that is described in the comment below. Now the point is that is $u$ is the measure sequence in $V$, then there is $\sigma: ORD \to V$ so that $\sigma(\alpha)=j_{0, \alpha}(u)\restriction \beta_\alpha,$ for some suitable $\beta_\alpha$ and such that for any $\alpha, \sigma \restriction \alpha+1$ is $\mathbb{R}_{\sigma(\alpha)}$-generic over $M_\alpha$.