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A generalization of the quotient integral formula is presented and some of its properties are investigated. Also the relations between two function spaces related to the spacial homogeneous spaces are derived by using general quotient integral formula. Finally our results are supported by some examples.

Let H be a compact subgroup of a locally compact group G. In this paper we define a convolution on M (G/H), the space of all complex bounded Radon measures on the homogeneous space G/H. Then we prove that the measure space M (G/H, * ) is a non-unital Banach algebra that possesses an approximate identity. Finally, it is shown that the Banach algebra M (G/H, * ) is not involutive and also L 1 (G/H, * ) is a two-sided ideal of it.

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