Pettis Integration

DOI10.2307/2044321zbMath0506.28007OpenAlexW4231135606MaRDI QIDQ4743034

Robert F. Geitz

Publication date: 1981

Full work available at URL: https://doi.org/10.2307/2044321

zbMATH Keywords

perfect measurePettis integrableVitali's convergence theoremBochner integrablestrongly integrableweakly measurable

Mathematics Subject Classification ID

Vector-valued set functions, measures and integrals (28B05) Vector-valued measures and integration (46G10)

Related Items

Weak and pseudo-solutions of an arbitrary (fractional) orders differential equation in nonreflexive Banach space ⋮ On the set of solutions of the Cauchy problem in Banach spaces ⋮ Multiparameter Persistence Landscapes ⋮ On the theory of fractional calculus in the Pettis-function spaces ⋮ On the nonlinear hammerstein integral equations in Banach spaces and application to the boundary value problem of fractional order ⋮ Multi-term fractional differential equation in reflexive Banach space ⋮ Fixed Point Theorems for Weakly Asymptotically Regular Mappings in Banach Spaces with an Application ⋮ On solutions of fractional order boundary value problems with integral boundary conditions in Banach spaces ⋮ Approximate Fixed Point Theory for Countably Condensing Maps and Multimaps and Applications ⋮ Unnamed Item ⋮ The weak McShane integral ⋮ Linear operators associated with \(p\)-Dunford, \(p\)-Pettis and \(p\)-Bochner integrable functions with values in a Banach space ⋮ On the lack of equivalence between differential and integral forms of the Caputo-type fractional problems ⋮ Fixed point theorems for convex-power condensing operators relative to the weak topology and applications to Volterra integral equations ⋮ Fixed point theory for countably weakly condensing maps and multimaps in non-separable Banach spaces ⋮ Geometry and the Pettis Integral ⋮ Second order three-point boundary value problems in abstract spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Krasnosel'skii-type fixed point theorems with applications to Volterra integral equations ⋮ On solutions of differential equations in Banach spaces ⋮ On the fractional calculus in abstract spaces and their applications to the Dirichlet-type problem of fractional order ⋮ Remarks on Pettis Integrability ⋮ The set of solutions of Volterra and Urysohn integral equations in Banach spaces ⋮ THE SET OF SOLUTIONS OF INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES ⋮ The Henstock-Kurzweil-Pettis Integrals and Existence Theorems for the Cauchy Problem ⋮ On the fractional order \(m\)-point boundary value problem in reflexive Banach spaces and weak topologies ⋮ On the weak solutions of a coupled system of Volterra--Stieltjes integral equations ⋮ Weak solutions of ordinary differential equations in Banach spaces ⋮ The multiplier for the weak McShane integral ⋮ On the weak solution $u ∈ C_1-α(I,E) of a fractional-order weighted Cauchy type problem in reflexive Banach spaces ⋮ Hadamard-type fractional calculus in Banach spaces ⋮ Unnamed Item ⋮ A Decomposition of Bounded Scalarly Measurable Functions taking their Ranges in Dual Banach Spaces ⋮ \(\mathfrak{S}\)-uniform scalar integrability and strong laws of large numbers for Pettis integrable functions with values in a separable locally convex space ⋮ Unnamed Item ⋮ Strong law of large numbers of Pettis-integrable multifunctions ⋮ Fixed point theory of Mönch type for weakly sequentially upper semicontinuous maps

Cites Work

• Unnamed Item
• Pointwise compact sets of measurable functions
• A decomposition theorem for additive set-functions with applications to Pettis integrals and ergodic means
• Weak compactness and reflexivity
• On perfect measures
• On Integration in Vector Spaces
• Integration in a Convex Linear Topological Space
• A decomposition of additive set functions