RT Journal Article
T1 Lineability, algebrability, and sequences of random variables
A1 Fernández Sánchez, Juan
A1 Seoane Sepúlveda, Juan Benigno
A1 Trutschnig, Wolfgang
AB We show that, when omitting one condition in several well-known convergence results from probability and measure theory (such as the Dominated Convergence Theorem, Fatou's Lemma, or the Strong Law of Large Numbers), we can construct “very large” (in terms of the cardinality of their systems of generators) spaces and algebras of counterexamples. Moreover, we show that on the probability space $([0,1],\mathcal {B}([0,1]),\lambda )$ the families of sequences of random variables converging in probability but (i) not converging outside a set of measure 0 or (ii) not converging in arithmetic mean are also “very large”.
PB Wiley
SN 0025-584X
YR 2022
FD 2022-03-20
LK https://hdl.handle.net/20.500.14352/72025
UL https://hdl.handle.net/20.500.14352/72025
LA eng
NO Ministerio de Ciencia e Innovación (MICINN)
DS Docta Complutense
RD 9 abr 2025