Let $G$ be a real Lie group and $X$ a real analytic manifold. Suppose that $G$ acts analytically on $X$ with finitely many orbits. Then the orbits are subanalytic in $X$. As a consequence we show that the micro-support of a $G$-equivariant sheaf on $X$ is contained in the conormal variety of the $G$-action.

MSC Classifications:

32B20, 22E15 show english descriptions Semi-analytic sets and subanalytic sets [See also 14P15]
General properties and structure of real Lie groups 32B20 - Semi-analytic sets and subanalytic sets [See also 14P15]
22E15 - General properties and structure of real Lie groups

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