Abstract
Let G be a Lie group, H ≤ G a closed subgroup and M ≈ G/H. In [14] André Weil gave a necessary and sufficient condition for the existence of invariant measures on homogeneous spaces of arbitrary locally compact groups. For Lie groups using the structure theory we give a neater necessary and sufficient condition for the existence of a G-invariant measure on M, cf. Theorems (2.1) and (3.2) in the introduction.
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Aithal, V.T., Kulkarni, R.S. On existence of invariant measures. Indian J Pure Appl Math 43, 343–358 (2012). https://doi.org/10.1007/s13226-012-0021-4
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DOI: https://doi.org/10.1007/s13226-012-0021-4