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Here, $\\mu^{\\beta}$ is the law of the standard Brownian bridge $\\beta$, while $\\rho^a$ and $\\rho$ denote densities which are given by $\\rho^a(z) := \\mathbf{1}_{[0,\\infty)}(\\bar{z}_a)$ and $\\rho(z) := \\int_0^1 \\mathbf{1}_{[0,\\infty)}(\\bar{z}_x) \\, dx$, respectively, for all $z\\in L^2(0,1)$ which have a (unique) continuous representative $\\bar{z}$ which vanishes at zero and one. 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Here, $\\mu^{\\beta}$ is the law of the standard Brownian bridge $\\beta$, while $\\rho^a$ and $\\rho$ denote densities which are given by $\\rho^a(z) := \\mathbf{1}_{[0,\\infty)}(\\bar{z}_a)$ and $\\rho(z) := \\int_0^1 \\mathbf{1}_{[0,\\infty)}(\\bar{z}_x) \\, dx$, respectively, for all $z\\in L^2(0,1)$ which have a (unique) continuous representative $\\bar{z}$ which vanishes at zero and one. 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