## Equivalences or singularity of Gaussian measures on function spaces |

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### Contents

The theory of reproducing kernels | 5 |

h Application of the theory of reproducing kernels | 21 |

The information function | 34 |

6 other sections not shown

### Common terms and phrases

a,bj absolutely continuous bounded linear operator bounded variation class F closed subspace complete orthonormal system continuous with respect Corollary corresponding covariance function dV(u dX(t E1 log eigenvalues eigenvectors equivalence or singularity exists expression F and F fulfilled functions f Gaussian measures Gaussian process Gaussian variables give hence Hilbert-Schmidt operator implies independent increments inner product Kakutani Kakutani's result lemma Let P1 Let us assume log p'(uj martingale mean value functions measurable space measures are equivalent non-singular Ornstein-Uhlenbeck process positive definite probability measures process with mean process X(t product measures proof prove remark reproducing kernel restrictions self-adjoint self-adjoint operator sequence Sf(t stationary processes stochastic integral term converges theorems 7.2 triangular covariances twice continuously differentiable v(svt Var1 Var2 Wiener-integral