Projective limits of measure preserving transformations on probability spaces

Some Observations on Dirac Measure-Preserving Transformations and their Results

Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measure-preserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac ...

Measure Preserving Transformations

This gives us a new probability measure on (Ω,F), so we may define expectations with respect to this conditioned probability measure. Thus for F measurable Y : Ω → R we define the conditional expectation E[Y | X = x] by taking the expectation of Y with respect to the measure (1.1). Consider now how to generalize the idea of conditional probability to the case when P (X = x) = 0. We wish to do t...

Determinant preserving transformations on symmetric matrix spaces

Let Sn(F) be the vector space of n × n symmetric matrices over a field F (with certain restrictions on cardinality and characteristic). The transformations φ on the space which satisfy one of the following conditions: 1. det(A+ λB) = det(φ(A) + λφ(B)) for all A,B ∈ Sn(F) and λ ∈ F; 2. φ is surjective and det(A+ λB) = det(φ(A) + λφ(B)) for all A,B and two specific λ; 3. φ is additive and preserv...

Projective limits of topological vector spaces

Laplace transform identities and measure-preserving transformations on the Lie-Wiener-Poisson spaces

Given a divergence operator δ on a probability space such that the law of δ(h) is infinitely divisible with characteristic exponent h 7→ − 2 ∫ ∞ 0 htdt, or ∫ ∞ 0 (e − ih(t)− 1)dt, h ∈ L(R+), (0.1) we derive a family of Laplace transform identities for the derivative ∂E[eλδ(u)]/∂λ when u is a non-necessarily adapted process. These expressions are based on intrinsic geometric tools such as the Ca...