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Given a closed bounded set $X \subset \mathbb{R}^3$ and two curves $\gamma_1$ and $\gamma_2$ in the group of orientation preserving isometries of $\mathbb{R}^3$. Define the sets $X_1$ and $X_2$ as the infinite intersections $X_1 = \bigcap_{p \in \gamma_1} pX$ and $X_2 = \bigcap_{q \in \gamma_2} qX$ where $kX$ represents the set $X$ transformed by $k$. If each of the $pX$ and $qX$ are measurable sets with measure $\mu$ defined on $\mathbb{R}^3$, and for each $p \in \gamma_1$ there exists a distinct $q \in \gamma_2$ such that $\mu(X \cap pX) \ge \mu(X \cap qX)$, can I conclude that $X_2 \mu(X_2) \subseteq X1$ le \mu(X_1)$ ? How so/ Why not? (We can assume the identity element of the isometry group is in both $\gamma_1$ and $\gamma_2$ if needed)

EDIT: Changed conclusion from $X_2 \subseteq X_1$ to $\mu(X_2) \le \mu(X_1)$ per Andreas Blass's comment.
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Measure of infinite intersection of sets

Given a closed bounded set $X \subset \mathbb{R}^3$ and two curves $\gamma_1$ and $\gamma_2$ in the group of orientation preserving isometries of $\mathbb{R}^3$. Define the sets $X_1$ and $X_2$ as the infinite intersections $X_1 = \bigcap_{p \in \gamma_1} pX$ and $X_2 = \bigcap_{q \in \gamma_2} qX$ where $kX$ represents the set $X$ transformed by $k$. If each of the $pX$ and $qX$ are measurable sets with measure $\mu$ defined on $\mathbb{R}^3$, and for each $p \in \gamma_1$ there exists a distinct $q \in \gamma_2$ such that $\mu(X \cap pX) \ge \mu(X \cap qX)$, can I conclude that $X_2 \subseteq X1$ ? How so/ Why not? (We can assume the identity element of the isometry group is in both $\gamma_1$ and $\gamma_2$ if needed)