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Cardinal characteristics of the ideal of Haar null sets

Taras O. Banakh (2004)

Commentationes Mathematicae Universitatis Carolinae

We calculate the cardinal characteristics of the σ -ideal 𝒩 ( G ) of Haar null subsets of a Polish non-locally compact group G with invariant metric and show that cov ( 𝒩 ( G ) ) 𝔟 max { 𝔡 , non ( 𝒩 ) } non ( 𝒩 ( G ) ) cof ( 𝒩 ( G ) ) > min { 𝔡 , non ( 𝒩 ) } . If G = n 0 G n is the product of abelian locally compact groups G n , then add ( 𝒩 ( G ) ) = add ( 𝒩 ) , cov ( 𝒩 ( G ) ) = min { 𝔟 , cov ( 𝒩 ) } , non ( 𝒩 ( G ) ) = max { 𝔡 , non ( 𝒩 ) } and cof ( 𝒩 ( G ) ) cof ( 𝒩 ) , where 𝒩 is the ideal of Lebesgue null subsets on the real line. Martin Axiom implies that cof ( 𝒩 ( G ) ) > 2 0 and hence G contains a Haar null subset that cannot be enlarged to a Borel or projective Haar null subset of G . This gives a negative (consistent) answer to a question of...

Category measures on Baire spaces.

José María Ayerbe Toledano (1990)

Publicacions Matemàtiques

The purpose of this paper is to give a necessary and sufficient condition to define a category measure on a Baire topological space. In the last section we give some examples of spaces in these conditions.

Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space

Jae Gil Choi, Sang Kil Shim (2023)

Czechoslovak Mathematical Journal

We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space ( H , B , ν ) . An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space B . Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur...

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