Since this is lesswrong let me try to explain with probability.
If you have a random variable X then you have an associated measure:
measure(A) = probability that X is in A.
If X has a probability density function f then:
measure(A) = integral over A of f = probability that X is in A
If you measure has an associated density then you can visualize it by visualizing the probability density function.
You get the Dirac measure if X is constant. Your random variable X always returns the same result. The associated pdf is the Dirac delta ‘function’. Sometimes people visualize the Dirac delta as an infinitely tall and infinitely thin Gaussian.
Since this is lesswrong let me try to explain with probability.
If you have a random variable X then you have an associated measure:
measure(A) = probability that X is in A.
If X has a probability density function f then:
measure(A) = integral over A of f = probability that X is in A
If you measure has an associated density then you can visualize it by visualizing the probability density function.
You get the Dirac measure if X is constant. Your random variable X always returns the same result. The associated pdf is the Dirac delta ‘function’. Sometimes people visualize the Dirac delta as an infinitely tall and infinitely thin Gaussian.
Does this make sense?