En este trabajo se estudia la topología de Redfield (R-topología) en el espacio de las medidas finitas y regulares sobre un espacio topológico numerable en el infinito. Para ello debemos estudiar bajo qué condiciones suficientes se puede asegurar que una medida bivalorada es exactamente una carga puntual. En general esta afirmación no es cierta y de ahí las condiciones restrictivas impuestas sobre el tipo de medidas y sobre la naturaleza del espacio topológico en lo que se refiere a la compacidad.Los...

Let $X$ be a completely regular $T_1$ space, $E$ a boundedly complete vector lattice, $C\left(X\right)$$(C_b(X...$

In this paper the problem of the existence of an inverse (or projective) limit measure ${\mu }^{\text{'}}$ of an inverse system of measure spaces $(X_i,{\mu }_i)$ is approached by obtaining first a measure $\tilde{\mu }$ on the whole product space ${\prod }_{i\in I}{X}_i$.The measure $\tilde{\mu }$ will have many of the properties of a limit measure provided only that the measures ${\mu }_i$ possess mild regularity properties.It is shown that ${\mu }^{\text{'}}$ can only exist when $\tilde{\mu }$ is itself a “limit” measure in a more general sense, and that ${\mu }^{\text{'}}$ must then be the restriction of $\tilde{\mu }$ to the projective limit...

It is proved that if X is infinite-dimensional, then there exists an infinite-dimensional space of X-valued measures which have infinite variation on sets of positive Lebesgue measure. In term of spaceability, it is also shown that $ca(ℬ,\lambda ,X)\setminus M_{\sigma }$, the measures with non-σ-finite variation, contains a closed subspace. Other considerations concern the space of vector measures whose range is neither closed nor convex. All of those results extend in some sense theorems of Muñoz Fernández et al. [Linear Algebra Appl....