Register to reply

Probability measure on smooth functions

by Tac-Tics
Tags: functions, measure, probability, smooth
Share this thread:
Tac-Tics
#1
Oct6-10, 12:00 AM
P: 810
Is there a "standard" probability measure one would use for the set of smooth real-valued functions on [a, b]?

My intuition is picturing a setup where you cut out shapes in the x-y plane, and then the set of functions whose graphs are contained in that shape have a measure proportional to the Euclidean area of the shape. But I can't quite make that intuition exact.
Phys.Org News Partner Science news on Phys.org
Flapping baby birds give clues to origin of flight
Prions can trigger 'stuck' wine fermentations, researchers find
Socially-assistive robots help kids with autism learn by providing personalized prompts
Eynstone
#2
Oct7-10, 06:10 AM
P: 336
Do you have the Borel measure ( under the sup metric ) in mind?
simeonsen_bg
#3
Oct8-10, 10:16 AM
P: 9
I suppose, you have to consider functions uniformely bounded by some constant M (or even vith uniformely bounded variation?), otherwise the whole set gets infinite measure, not 1, the way you described the measure.


Register to reply

Related Discussions
Smooth non analytic functions Calculus 10
Piecewise smooth functions Calculus & Beyond Homework 1
Smooth Functions Calculus & Beyond Homework 2
Question about extentions of smooth functions Calculus 3
Clairaut's theorem and smooth functions Calculus 2