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On Hyperfinite Representations of Distributions
Author(s) -
Kessler Christoph
Publication year - 1988
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/20.2.139
Subject(s) - mathematics , statistical physics , econometrics , physics
It is shown that an internal step function on an s ‐dense ‘time line’ approximating a Schwartz distribution is not necessarily invariant under internal infinitesimal permutations of the arguments. This invariance holds exactly if the step function is near standard as a signed σ‐additive Radon measure.