Plans at a Square-Integrable Noncommutative Law

In the setting of Plan Jets and Hamiltonians on Square-Integrable Noncommutative Laws: Standing Notation, let $\mu\in\Sigma^{2}_{d}$.

¶A plan at $\mu$ is an $L^{2}$ law $\pi\in\Sigma^{2}_{2d}$ whose push-forward under the marginal datum $\mathrm{pr}^{1}$ is $\mu$, that is, $\mathrm{pr}^{1}_{\#}\pi=\mu$.