积分, VII, p. 88
令G \mathfrak{G} G G \mathfrak{G} G G G G H H H s = ξ x = y η s = \xi x = y \eta s = ξ x = y η ( ξ , η ∈ G , x , y ∈ H ) (\xi, \eta \in G,\ x, y \in H) ( ξ , η ∈ G , x , y ∈ H ) s ∈ G s \in \mathfrak{G} s ∈ G ξ , x , y , η \xi, x, y, \eta ξ , x , y , η s s s ξ ∈ G \xi \in G ξ ∈ G ξ ^ \widehat{\xi} ξ ξ x ∈ ξ ^ ( x ) G ( x ∈ H ) \xi x \in \widehat{\xi}(x)G\ (x \in H) ξ x ∈ ξ ( x ) G ( x ∈ H ) x ∈ H x \in H x ∈ H x ^ \widehat{x} x ξ x ∈ H x ^ ( ξ ) ( ξ ∈ G ) \xi x \in H \widehat{x}(\xi)\ (\xi \in G) ξ x ∈ H x ( ξ ) ( ξ ∈ G ) μ , α , β \mu, \alpha, \beta μ , α , β G , G , H \mathfrak{G}, G, H G , G , H
d x ^ − 1 ( α ) ( ξ ) = Δ G ( ξ ^ ( x ) ) Δ G ( x ^ ( ξ ) ) Δ H ( ξ ^ ( x ) ) Δ G ( ξ ) d α ( ξ ) ,
d\widehat{x}^{-1}(\alpha)(\xi) = \frac{\Delta_{\mathfrak{G}}(\widehat{\xi}(x)) \Delta_G(\widehat{x}(\xi))}{\Delta_H(\widehat{\xi}(x)) \Delta_G(\xi)} d\alpha(\xi),
d x − 1 ( α ) ( ξ ) = Δ H ( ξ ( x )) Δ G ( ξ ) Δ G ( ξ ( x )) Δ G ( x ( ξ )) d α ( ξ ) , d ξ ^ − 1 ( β ) ( x ) = Δ G ( x ^ ( ξ ) ) Δ G ( x ^ ( ξ ) ) d β ( x ) .
d\widehat{\xi}^{-1}(\beta)(x) = \frac{\Delta_G(\widehat{x}(\xi))}{\Delta_{\mathfrak{G}}(\widehat{x}(\xi))} d\beta(x).
d ξ − 1 ( β ) ( x ) = Δ G ( x ( ξ )) Δ G ( x ( ξ )) d β ( x ) . （令 f ∈ K ( G ) f \in \mathscr{K}(G) f ∈ K ( G ) ∫ f ( u ) d μ ( u ) \int f(u) d\mu(u) ∫ f ( u ) d μ ( u ) X = G , Y = H X = G,\ Y = H X = G , Y = H X = H , Y = G X = H,\ Y = G X = H , Y = G f f f