Teorema de existencia y representación integral del producto tensorial de medidas vectoriales
The Bessaga-Pelczynski Property and Strongly Bounded Measures
The Bishop-Phelps theorem and the RNP
The Bochner and the monotone integrals with respect to a nuclear-valued finitely additive measure
The dual of every Asplund space admits a projectional resolution of the identity
The general Fubini theorem in complete bornological locally convex spaces.
The Kluvanek-Kantorovitz characterization of scalar operators in locally convex spaces.
The McShane, PU and Henstock integrals of Banach valued functions
Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals...
The multiplier for the weak McShane integral
The multiplier for the weak McShane integral which has been introduced by M. Saadoune and R. Sayyad (2014) is characterized.
The Nikodym theorems for operator measures.
The precompactness–lemma
The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of
Let (S, ∑, m) be any atomless finite measure space, and X any Banach space containing a copy of . Then the Bochner space is uncomplemented in ccabv(∑,m;X), the Banach space of all m-continuous vector measures that are of bounded variation and have a relatively compact range; and ccabv(∑,m;X) is uncomplemented in cabv(∑,m;X). It is conjectured that this should generalize to all Banach spaces X without the Radon-Nikodym property.
The Radon--Nikodym theorem for reflexive Banach spaces.
The Radon-Nykodym property
The range of vector measures into Orlicz spaces
The theory of stationary vector-valued measures over R.
The Vitali convergence theorem for the vector-valued McShane integral
The classical Vitali convergence theorem gives necessary and sufficient conditions for norm convergence in the space of Lebesgue integrable functions. Although there are versions of the Vitali convergence theorem for the vector valued McShane and Pettis integrals given by Fremlin and Mendoza, these results do not involve norm convergence in the respective spaces. There is a version of the Vitali convergence theorem for scalar valued functions defined on compact intervals in given by Kurzweil and...
The weak McShane integral
We present a weaker version of the Fremlin generalized McShane integral (1995) for functions defined on a -finite outer regular quasi Radon measure space into a Banach space and study its relation with the Pettis integral. In accordance with this new method of integration, the resulting integral can be expressed as a limit of McShane sums with respect to the weak topology. It is shown that a function from into is weakly McShane integrable on each measurable subset of if and only if...
The weak Radon-Nikodym property
The weak Radon-Nikodym property in Banach spaces