Vol. 100, No. 2, 1982

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ISSN: 0030-8730
Maximal functions for a semiflow in an infinite measure space

Ryōtarō Satō

Vol. 100 (1982), No. 2, 437–443
Abstract

Let (X,) be a σ-finite measure space and Γ = (𝜃t : t 0) a measurable semiflow of measure preserving transformations on (X,). The maximal function f of a function f L1(μ) + L(μ) is defined by

 ∗        1 ∫ b
f (x) = sbu>p0 b 0 |f(𝜃tx )|dt.

The purpose of this paper is to prove that if μ(X) = and the semiflow Γ is conservative and ergodic then for every constant α > 0

             ∫
α μ{f∗ > α } =      |f|dμ.
{f∗>α}

Mathematical Subject Classification 2000
Primary: 28D10
Milestones
Received: 20 August 1980
Published: 1 June 1982
Authors
Ryōtarō Satō