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This paper shows that a formula for the pushforward measures on the fiber bundle \( G \rightarrow G / H \) of homogeneous space of locally compact groups G and H can be written down by using the modular functions. As a result, we obtain the equality \(\begin{aligned} \frac{ \Delta _G ( h ) }{ \Delta _{ G / N } ( h N ) } = \frac{ \Delta _H ( h ) }{ \Delta _{ H / N } ( h N ) } \end{aligned}\) on the modular functions for any closed subgroups N and H of a locally compact group G with \( N \lhd G \) and \( N \subset H \subset G \) and any \( h \in H \) .

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Pushforward Measures on Homogeneous Spaces of Non-unimodular Groups and Properties of Modular Functions

  • 会议论文

  • 发表日期：

    2026年

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  • Takashi Satomi

摘要

This paper shows that a formula for the pushforward measures on the fiber bundle \( G \rightarrow G / H \) of homogeneous space of locally compact groups G and H can be written down by using the modular functions. As a result, we obtain the equality \(\begin{aligned} \frac{ \Delta _G ( h ) }{ \Delta _{ G / N } ( h N ) } = \frac{ \Delta _H ( h ) }{ \Delta _{ H / N } ( h N ) } \end{aligned}\) on the modular functions for any closed subgroups N and H of a locally compact group G with \( N \lhd G \) and \( N \subset H \subset G \) and any \( h \in H \) .