Pathological Properties of Weak L^p Spaces

Ali Farokhinia; Ali Rastegar

Ali Farokhinia Dept. of Math. Islamic Azad University, Shiraz Branch, Shiraz, Iran
Ali Rastegar Dept. of Math., Shiraz Branch, Islamic Azad University, Shiraz, Iran

Keywords: Algebrability, Lineability, Pathological Properties, Weak Lp.

Abstract

Weak 𝐿^𝑝 spaces, that are shown through this paper by 𝐿^𝑝_w , are function spaces that are closed to 𝐿^𝑝 spaces, but somehow larger. The question that we are going to partially answer in this paper, is that how much it is larger. Actually we prove that 𝐿^𝑝_w (ℝ) ∖ 𝐿^𝑝 (ℝ) ∪{0} contains an infinitely generated algebra.

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