TY - JOUR
A2 - Gallardo Gutiérrez, Eva A.
AU - Bartoszewicz, Artur
AU - Bienias, Marek
AU - Głąb, Szymon
PY - 2018
DA - 2018/12/04
TI - Lineability within Peano Curves, Martingales, and Integral Theory
SP - 9762491
VL - 2018
AB - This paper is devoted to give several improvements of some known facts in lineability approach. In particular, we prove that (i) the set of continuous mappings from the unit interval onto the unit square contains a closed, c-semigroupable convex subset, (ii) the set of pointwise convergent martingales (Xn)n∈N with EXn→∞ is c-lineable, (iii) the set of martingales converging in measure but not almost surely is c-lineable, (iv) the set of sequences (Xn)n∈N of independent random variables, with EXn=0, ∑n=1∞var Xn=∞, and the property that (X1+⋯+Xn)n∈N is almost surely convergent, is c-lineable, (v) the set of bounded functions f:[0,1]×[0,1]→R for which the assertion of Fubini’s Theorem does not hold is consistent with ZFC 1-lineable (it is not 2-lineable), (vi) the set of unbounded functions f:[0,1]×[0,1]→R for which the assertion of Fubini’s Theorem does not hold (with infinite integral allowed) is c-lineable but not c+-lineable.
SN - 2314-8896
UR - https://doi.org/10.1155/2018/9762491
DO - 10.1155/2018/9762491
JF - Journal of Function Spaces
PB - Hindawi
KW -
ER -