In measure theory, a null set refers to a set of measure zero. For example, in the reals, 
with its standard measure (Lebesgue measure), the set of rationals 
has measure 
, so 
is a null set in 
. Actually, all finite and countably infinite subsets of 
have measure 
. In contrast, the empty set always refers to the unique set with no elements, denoted 
, 
or 
.
measure theory - Difference between Null set and empty set - Mathematics Stack Exchange
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In measure theory, a null set refers to a set of measure zero. For example, in the reals, with its standard measure (Lebesgue measure), the set of rationals has measure , so is a null set in . Actually, all finite and countably infinite subsets of have measure . In contrast, the empty set always refers to the unique set with no elements, denoted , or .
They aren't the same although they were used interchangeable way back when.
In mathematics, a null set is a set that is negligible in some sense. For different applications, the meaning of "negligible" varies. In measure theory, any set of measure 0 is called a null set (or simply a measure-zero set). More generally, whenever an ideal is taken as understood, then a null set is any element of that ideal.
Whereas an empty set is defined as:
In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced. Many possible properties of sets are trivially true for the empty set.
In analysis and measure theory, the term null set is also used to denote a set which has "size" zero, but in that case, size means a different thing. For instance, on the real line, it is customary to use length (at least in naïve settings). So the interval $[-3, 5]$ has size $8$ and the set $(2, 3)\cup [5, 7]$ has size $3$.
In this setting, examples of non-empty null-sets are:
- Single-element sets, like $\{5\}$.
- In fact, any countable set, like $\Bbb Q$
- The Cantor set
So whether there is a difference between the phrases "empty set" and "null set" depends entirely on the context.
This depends on the context.
In the context of set theory, the null set is the empty set. And that's the end of it.
In the context of measure theory, analysis, or probability, a null set is a set whose measure is $0$. For example in the usual Borel measure, finite sets are null sets; countable sets are null sets; and even some uncountable sets (e.g. the Cantor set) are null sets. But they are certainly not empty.
In that context, a null set is a set which is completely uninteresting "for practical purposes" and we can ignore safely ignore it if we choose to. So this statement is more general than just "empty".
Note, however, that if you define an equivalence relation "$A\sim B$ if and only if $A\mathbin{\triangle}B$ is a null set", then the null sets are exactly those equivalent to the empty set.
<[]> means an object include no elements. null is not an element.
after u call Structure method like new HashSet<>();, set point to a real memory. But null point to nowhere.
A set containing null contains the element null. An empty set does not contain the element null.
Suppose you make a set containing null like this:
Set<Object> setWithNull = new HashSet<Object>();
setWithNull.add(null);
And an empty set like this:
Set<Object> emptySet = new HashSet<Object>();
Then you can see the following differences:
setWithNull.size()==1 emptySet.size()==0
setWithNull.isEmpty()==false emptySet.isEmpty()==true
setWithNull.contains(null)==true emptySet.contains(null)==false
setWithNull.equals(emptySet)==false
So a set containing null is different from an empty set in many significant ways.